CAT Percentages questions (2017–2025) — actual Quant questions with solutions

The average salary of 5 managers and 25 engineers in a company is Rs 60000. If each of the manager receive 20% hike in the salary while the salary of the engineer remains unchanged , the average salary of all 30 employees increased by 5%.The average salary, of engineer , in rs , is :

Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. The total time taken is 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, required to walk from A to B and run from B to C is: [TITA]

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is

A loan of Rs 1000 is fully repaid by two instalments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is _____

A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of the resulting solution with water, and finally replaces 10% of this solution with acid, then 15% of the solution obtained with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was _____

A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to the customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is

Mixtures + Percentages + Ratios

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Percentages + Averages + Equations

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40,000, of the last 30 employees was Rs. 60,000, and of the first 10 and last 10 employees together was Rs. 50,000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

Ratios + Percentages

In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 ∶ 6 ∶ 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to?

Gopal’s salary becomes 187.5% of original after two successive increments. The second increment is twice the first. Find the percentage increase in the first increment.

The population of a town in 2020 was 100,000. The population decreased by \( y\% \) from 2020 to 2021, and increased by \( x\% \) from 2021 to 2022. If the population in 2022 was greater than in 2020 and \( x - y = 10 \), what was the lowest possible population in 2021?

CAT 2022 Slot 3 - Question 5

Nitu has an initial capital of ₹20,000 . Out of this, she invests ₹8,000 at 5.5% in bank A,₹5,000 at 5.6% in bank B and the remaining amount at x% in bank C , each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

CAT 2022 QA Slot-2 Question 1

In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted vote while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was:

CAT 2022 Slot 2 - Question 6

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

CAT QA 2021 Slot-3 Question 3

In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be

CAT QA 2021 Slot- 3 Question 4

The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is

CAT QA 2021 Slot-2 Question 2

Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

CAT 2020 Slot 2 Question 7

In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent 450 on rice in April, then how much did he spend on wheat in May?

CAT 2020 Slot 1 Question 8

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

CAT 2019 Slot 2 Question 9

In 2010, a library contained a total of 11500 books in two categories − fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

CAT 2019 Slot 2 Question 10

In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was

CAT 2019 Slot 1 Question 11

In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys,pass an examination, the percentage of the girls who do not pass is

CAT 2019 Slot 1 Question 12

Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is

CAT 2019 Slot 1 Question 13

The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes down by 4% and Bimala's goes up by 10%, then the percentage by which Kamala's income would exceed Bimala's is nearest to

CAT 2017 Slot 2 Question 14

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

CAT 2017 Slot 1 - Question 15

Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?