Preparing for the CAT requires more than just understanding concepts—it demands consistent practice, smart application, and the ability to spot traps under time pressure. To keep your prep exciting and razor-sharp, welcome to the Weekly CAT Prep Challenge! Every week, we’ll hand-pick questions from key Quant topics that test both your fundamentals and your problem-solving instincts.
This week’s challenge is based on a topic that shows up across multiple areas of the CAT Quant section—Percentages.
Why Percentages?
Percentages aren’t just a standalone topic. They are the foundation for topics like Profit & Loss, Data Interpretation, Mixtures & Alligations, and more. CAT loves testing percentages subtly, often through layered conditions or percentage change scenarios that require a deep understanding of base value and effective change.
Your Challenge: Solve These Questions
Try solving the following questions without a calculator. Time yourself for an extra challenge. Solutions are provided at the end for reference.
Q1. Ravi’s monthly salary is A rupees. Of this, he spends x% in the first month. The next month he has an increase of C% in his salary and D% in his expenditure. The new amount saved is:
(a) A(1 + C/100) – X(1 + D/100)
(b) A(1 + C/100) (C – D)/100
(c) X(C – D)/100
(d) X(C + D)/100
Q2. A batsman scored 100 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Q3. A man invests ₹ 10,000 in some shares in the ratio 2 : 3 : 5 which pay dividends of 10%, 25% and 20% (on his investment) for that year respectively. Find his dividend income.
(a) 1900
(b) 2000
(c) 2050
(d) 1950
Q4. Vicky’s salary is 75% more than Ashu’s. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky’s salary more than Ashu’s?
(a) 96%
(b) 51.1%
(c) 90%
(d) 52.1%
Q5. Mr. Abhimanyu Banerjee is worried about the balance of his monthly budget. The price of petrol has increased by 40%. By what percent should he reduce the consumption of petrol so that he is able to balance his budget?
(a) 33.33
(b) 28.56
(c) 25
(d) 14.28
Q6. A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due to this mistake.
(a) 96%
(b) 95%
(c) 2400%
(d) 200%
Q7. 50% of a% of b is 75% of b% of c. Which of the following is c?
(a) 1.5a
(b) 0.667a
(c) 0.5a
(d) 1.25a
Q8. A landowner increased the length a d the breadth of a rectangular plot by 10% and 20% respectively. Find the percentage change in the cost of the plot assuming land prices are uniform throughout his plot.
(a) 33%
(b) 35%
(c) 22.22%
(d) None of the above
Q9. The price of sugar is reduced by 25% but inspite of the decrease, Ajay ends up increasing his expenditure on sugar by 20%. What is the percentage change in his monthly consumption of sugar?
(a) +60%
(b) -10%
(c) +33.33%
(d) 50%
Q10. When 60% of a number A is added to another number B. B becomes 175% of it's previous value. The which of the following is true regarding the values of A and B?
(a) A>B
(b) B>A
(c) Either (a) or (b) depending upon the values of A and B
Q11. The population of a village is 1,00,000. The rate of increase is 10% per annum. Find the population at the start of third year.
(a) 1,33,100
(b) 1,21,000
(c) 1,18,800
(d) 1,20,000
Q12. In a class, 25% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 60 marks and the pass marks are 33 (counting the final scores of the candidates).
(a) 37.266
(b) 37.6
(c) 37.8
(d) 36.93
Q13. Last year, the Indian cricket team played 40 one-day cricket matches out of which they managed to win only 40%. This year, so far it has played some matches, which has made it mandatory for it to win 80% of the remaining matches to maintain its existing winning percentage. Find the number of matches played by India so far this year.
(a) 30
(b) 25
(c) 28
(d) Insufficient Information
Q14. Recently, while shopping in Patna market in Bihar, I came across two new shirts selling at a discount. I decided to buy one of them for my little boy Ankit. The shopkeeper offered me the first shirt for Rs 42 and said that it usually sold for 8/7 of that price. He then offered the other short for Rs 36 and said that it usually sold for 7/6th of that price. Of the two shirts which do you think is a better bargain and what is the percentage discount on it?
(a) first shirt, 12.5
(b) second shirt, 14.28
(c) Both are same
(d) None of these
Ready for More?
If you enjoyed solving these, bookmark this series! Next week we’ll dive into another core topic with a mix of concept-based and tricky questions that will keep your mind sharp and ready for D-Day.
Tip of the Week:
Whenever you see a percentage increase or decrease in two variables (like salary and expenditure), use successive percentage change logic or plug in simple values like 100 to test options. The CAT often tests logic over brute-force calculation.
Answer Key:
Q1. A
Q2. 40
Q3. D
Q4. A
Q5. B
Q6. A
Q7. B
Q8. D
Q9. A
Q10. C
Q11. B
Q12. B
Q13 D
Q14. B
Read More:
- DILR Strategies to Score a 99 Percentile
- Free Formula Book for Quants
- From a Failed UPSC Attempt to IIM-C
- From Journalism to IIM-K
- VARC Guide For Engineers
- 5 VARC Strategies to Begin Your Comprehension Game
- Staying consistent with the 6-month-long CAT journey
