Message Author

Dealing with Percentages – Part 2

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

Study Plan for CAT 2013: Part 2

This is Part 2 of Ravi Handa’s study plan for CAT 2013. (You can read Part 1 here)

The three big questions, which nearly every aspirant wants to know the answer to, are:

a)     In which order should I prepare?

b)     How much should I cover and by what date?

c)      When should I start taking mock tests?

The dates for the CAT 2013 exam (October 16 – November 11, 2013) were declared last week. There are a little over 5 months for you to prepare. The answers to the above questions are based upon that key information. I will not say that I know the perfect answers as they would vary from person to person. But I shall try to generalize.

In which order should I prepare?

The CAT syllabus could be divided into three broad areas:

  1. Verbal
  2. DI / LR
  3. Quant.

1. Verbal

This can once again be classified into two broad categories:

  • Reading Comprehension
  • Verbal Usage & Reasoning

Preparation for Reading Comprehension is something that you should start from day 1. You can start by doing small passages and studying the kind of passages that you are comfortable with and gradually move up to tougher passages and questions.

For Verbal Usage & Reasoning, it is recommended that you start with vocabulary building, move on to grammar and prepare for Verbal Reasoning in the end. You should not spend too much time on Vocabulary and Grammar but it is a good starting point. Also, you need to have a good handle on things before you start topics in Verbal Reasoning. It would be difficult to do well in Verbal Reasoning unless you are confident in vocabulary and have decent grammar.

2. Data Interpretation & Logical Reasoning

This section does not follow a fixed pattern. The questions and question types vary every year. You can start off with the easy stuff like bar charts, pie charts, etc. and move on to advanced / difficult questions in the later part of your preparation.

3. Quant.

It is probably the easiest part to structure in your preparation. It can be further classified into:

  • Number Systems
  • Arithmetic
  • Algebra
  • Geometry
  • Modern Maths (Progressions, Permutation & Combination, Set Theory)

You should study them in the order that is mentioned above. A very common mistake that I have seen students make is that they spend too much time on Number Systems & Modern Maths whereas they spend too little time on Algebra & Geometry. I think it is because it is easy to get fascinated by concepts in those two topics while Geometry & Algebra are, for the lack of a better word, boring. But then – you are not writing the CAT for amusement. You have Robert Downey Jr. for that. Do not make this mistake and give importance to all parts of Quantitative Aptitude.

How much should I cover and by what date?

 There is no correct date but some broad guidelines which should help.

  • By end of July, you should have covered the basics of all topics and should be able to solve easy questions / sitters from all topics.
  • August should be spent on analyzing and improving your weak areas. By end of August, you should be able to reach your peak understanding in all topics.
  • September should be spent solely on improving your speed and performance in tests.

When should I start taking mock tests?

 An ideal scheduling for mock-CATs would be:

2 in June

2 in July

3 in August

3 in September

Now some of you might be wondering that this is just 10 mock-CATs. Too few? I don’t think so. Ten tests are more than enough if you can analyze and improve your performance via these. You might have read on various forums and a lot of experts tell you to write as many mock tests as possible and that is the best way to prepare. I do not belong to that school of thought. I believe that attempting 10 mock-CATs and analyzing them is more than good enough for any aspirant.

Having said that, if you are someone who has written the CAT before and scored a 95+ percentile, you can go in for a higher number of mocks as the time you would need to spend on preparation is going to be much less.

I hope you found this post helpful. If you have any queries / suggestions for future posts, use the comment section.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)

 

Other articles by Ravi Handa can be found here


Ravi Handa

Message Author


Message Author

Study Plan for CAT 2013: Part 1

Let me start by saying, there is no such thing as a perfect study plan. There may be something like a good study plan but that will also vary from an individual to an individual. This post and the couple more which will follow are an exercise in generalization which should be taken as just that – a gross generalization rather than something written in stone. Having said that, this generalization might be able to throw some light in the right direction and might help you choose your path to success.

 

To begin with, I would like to define the CAT aspirants into two categories:

a)     Working Professionals

b)     Fresher

I know that there are plenty of aspirants who do not fit into either of the categories. So, think of the two categories as ‘Busy’ & ‘Free’. Now you might argue that as a Fresher / student you have workload of assignments, end-sems, project submissions, etc. Stop quibbling! If you do not have a boss breathing down on your neck asking you to submit the Weekly Estimated Net Usage System report on Monday morning, you are in the ‘Fresher’ category. On the contrary, if you are warming the benches of a mass recruiting soul sucking IT company – you are not in the ‘Working Professional’ category.

 

First things first, how much time is actually required to perform well in CAT. In my opinion, anything from 300 to 500 hours is more than enough preparation for CAT. You will be able to reach your peak performance in that space of time. The key idea is that this period of 300 to 500 hours should be spread over anywhere from 5 months to 10 months. Anything above that is overkill and students tend to lose focus. Anything less than 5 months, the students tend to panic. If you are reading this, the day it got published you are nicely poised to start your prep and take it to the next level. Do not be worried or concerned about being too late or too early. Whenever you start, is the right time. The idea is not to lose momentum in the middle – which happens way too often than you would imagine once the test series starts and people start getting disappointing scores.

 

Whatever I have said till now is valid for any CAT aspirant. As to what you should actually be doing, I believe a different approach is required for both categories. Today, I am going to talk about what should be done by ‘Working Professionals’.

 

As a ‘Working Professional’, you should try to find around 15 – 20 hours a week of study time. The key is that every day should try to find at least 1.5 to 2 hours with a little more on the weekend. If you already know what your strong / weak areas are: brilliant. You should devote majority of your time in clearing up your weak areas and building up your basics. In case you don’t, here is what I suggest.

Mon / Wed / Fri – Quant Basics

Tue – Verbal Basics

Thur – Reading Comprehension Basics

Saturday – Section 1 Application (Quant + DI)

Sunday – Section 2 Application (Verbal + LR)

As you might have noticed, there is no time which is devoted towards LR / DI basics. Well, that is because I don’t believe there is anything such as LR / DI basics. You should just practice questions of various Logical Reasoning / Data Interpretation.

 

If you are Fresher candidate, just multiply the time allocation with a factor of 1.5 and keep following the same plan.

 

With this I would like to wrap up this post. In my next post, I would try to answer the following questions:

a)     In which order you should prepare

b)     How much should you cover and by what date.

c)      When should you start your test series

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)

 

Other articles by Ravi Handa can be found here


Ravi Handa

Message Author


Message Author

Dealing with Percentages – Part 2

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author


Message Author

This is in continuation of my previous post. In case you haven’t gone through it, I suggest you read that first.

(You can read ‘Dealing with Percentages – Part 1‘ here)

In Part 1, I discussed the basic concepts, covering the following:

  • Percentage as Fractions
  • Percentage Change
  • Changing Quantities by Percent

I would like to discuss a few more ideas in this post. Let us begin.

Successive Percentage Change:

I am sure that you would have seen retail stores with offers like “50% + 40% off”. If my memory serves me right, these types of offers were made extremely popular by Koutons. I always thought of it as a “90% off” offer but clearly I was wrong. I guess some of you might have made the same mistake as well. A “50% + 40% off” does not mean a “90% off”. It actually means that you will be given a discount of 50% first and then on the reduced price you will be given another 40% discount.

Let us calculate to figure out how much this actually means.

Let us assume that the T-shirt you are trying to buy costs Rs. 100. A 50% discount would bring down the price of the T-shirt to Rs. 50. Another 40% discount on the reduced price of Rs. 50 would further bring down the price by Rs. 20 (which is 40% of 50), to Rs. 30. So, the price has effectively gone down from Rs. 100 to Rs. 30 which means that the effective discount has been 70% and not 90%.

Let me ask you another question. Try to answer it in your head before you actually scroll down and check the answer.

(Join the InsideIIM Test Prep group on Facebook here)

Example 1: 

Shop A is selling a T-shirt at a discount of 50% + 40% on the MRP whereas shop B is selling the same T-shirt at a discount of 40% + 50%. Should you buy the T-shirt from Shop A or Shop B?

Now, there may be a few things going on in your head like ‘A’ is better because it is offering the higher percentage first or ‘B’ is better because it is offering the higher percentage later or this cannot be determined until and unless we know the MRP of the T-shirt. Well, stop your internal monologue! The answer is that it would not make a difference whether you buy it from Shop A or from Shop B. Don’t believe me? Do the math!

Let us assume that the MRP of the T-shirt is ‘x’

From Shop A, a 50% discount would bring down the price to 0.5x and another 40% discount would bring down the price to 0.3x

From Shop B, a 40% discount would bring down the price to 0.6x and another 50% discount would bring down the price to 0.3x

As you can see, the sale price is the same in both cases.

In case you are wondering as to why it is the same in both cases, it is because percentages are multiplicative in nature and p*q is always the same as q*p.

For future reference, you can use this formula for effective % change in case of successive % changes of a% and b%:

Note: Please keep in mind the ‘+’ & ‘-’ signs while using this formula.

If you put a = 50% and b = 40% (from the above example), you would get 110%, which would be the incorrect answer. You should use -50% and -40% to get the correct answer of -70%. You will have to use negative values for the above example because the % changes considered are discounts.

Example 2:

A company’s revenue grew by 10% and 20% in 2009 and 2010 but fell by 25% in 2011. What was the net % change?

Use the formula for the first two years = 10 + 20 + 10*20/100 = 32

Combine this with the last year = 32 – 25 + (32)(-25)/100 = 7 – 8 = -1%

Compensating Percentage Change:

I am sure that you must have encountered questions like these:

a)     The price of beer has gone up by 25%. By how much should you reduce your consumption so that your expenses do not change?

b)     Ravi got a salary hike of 10%. The new boss thought this shouldn’t have happened because Ravi doesn’t deserve it, so he slashes Ravi’s salary by 10%. Is Ravi back to the original? If no, then by what % should Ravi’s boss reduce his salary?

Now there are a couple of ways of doing these questions. One is by using the concepts of fractions, proportionality, etc. The other one is by using the formula. Let us discuss both of them.

a)     Price of beer has gone up by 25%

  •  Price of beer has increased by 1/4th
  •  Price of beer has become 5/4th
  •  Consumption should become 4/5th
  •  Consumption should be reduced by 1/5th
  •  Consumption should be reduced by 20%

b)     A hike of 10% and then a reduction of 10% won’t be fair as Ravi would end up getting less than the original. Using the successive % change formula {10 – 10 + 10*(-10)/100 = -1}, we can say that he would end up getting 1% lesser than the original. To get the correct deduction value:

Ravi’s salary was hiked by 10%

  • Ravi’s salary has increased by 1/10th
  • Ravi’s salary has become 11/10th
  • To go back to the original, it should become 10/11th of the current value
  • It should be reduced by 1/11
  • It should be reduced by 9.09%

We could have also used the formula for compensating a change of r%:

a) r = 25%. Compensating % change =   – (100*25)/(100+25)

     –20% = reduction of 20%

b) r = 10%. Compensating % change =   – (100*10)/(100+10)

     –9.09% = reduction of 9.09%

 I hope that you found this post useful and that it will help you get a higher percentage and percentile in your exam.

– Ravi Handa

(Ravi Handa, an alumnus of IIT Kharagpur, has been working in the CAT Prep sector for the past 7 years. He currently offers online CAT coaching and preparation for CAT 2015)
Other articles by Ravi Handa can be found here

 


Ravi Handa

Message Author