CAT Ratio & Variation questions (2018–2025) — actual Quant questions with solutions

Breakup G Strategy: Ratios

The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were shifted from box A to box B, this ratio became 37:20. The number of coins to be further shifted from box A to box B to make this ratio 1:1 is: [TITA]

The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is

The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is

Ages + Ratios

When Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

Ratios + Simple Equations

A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is: ______ TITA

Ratios + Allegations

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

When Rajesh’s age was equal to Garima’s current age, their age ratio was 3:2. When Garima becomes Rajesh’s current age, what will be their age ratio?

Rajesh and Vimal own 20 and 30 hectares of land. Vimal grows wheat and mustard in 5:3 ratio. Total wheat:mustard ratio is 11:9. Find the wheat:mustard ratio in Rajesh’s land.

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.

A fruit seller has a total of 187 fruits consisting of apples, mangoes, and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes, and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is

Two collectors A and B collect coins weekly in the ratio 3:4. If A collects a multiple of 7 in 5 weeks and B collects a multiple of 24 in 3 weeks, what is the minimum number of coins collected by A in one week?

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is

In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is

One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, then Sunil’s share, in rupees, is

A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:3. Then Anjali's score exceeded Rama's score by

The salaries of Ramesh, Ganesh and Rajesh were in the ratio 6:5:7 in 2010, and in the ratio 3:4:3 in 2015. If Ramesh’s salary increased by 25% during 2010-2015, then the percentage increase in Rajesh’s salary during this period is closest to

Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250?

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio

The electrical current \( I \) (in amperes) in a simple circuit varies directly as the voltage \( V \). If the current is 5 A when the voltage is 15 V, what is the current when the voltage is 25 V?

The electrical current \( I \) in a conductor varies inversely as the resistance \( R \) (in ohms). If the current is 12 A when the resistance is 240 Ω, what is the current when the resistance is 540 Ω?

Hooke’s Law states that the distance \( s \) that a spring is stretched varies directly with the mass \( m \) of the object. If the spring stretches 18 cm with a 3 kg mass, how far will it stretch with a 5 kg mass?

The volume \( V \) of an ideal gas at constant temperature varies inversely with the pressure \( P \). If the volume is 200 cm³ at 32 kg/cm², what is the volume at 40 kg/cm²?

The number of aluminum cans \( c \) used each year varies directly as the number of people \( p \). If 250 people use 60,000 cans in one year, how many cans would 1,000,000 people use?

The time \( t \) to complete a masonry job varies inversely with the number of bricklayers \( b \). If 7 bricklayers can finish the job in 5 hours, how long would it take 10 bricklayers?

The wavelength \( \lambda \) of a radio signal varies inversely with its frequency \( f \). A wave with a frequency of 1200 kilohertz has a wavelength of 250 meters. What is the wavelength when the frequency is 60 kilohertz?

The amount of water \( w \) in a human body is directly proportional to the body mass \( m \). If a 96 kg person contains 64 kg of water, how much water is in a 60 kg person?

The time \( t \) to drive a fixed distance varies inversely with speed \( v \). If it takes 5 hours at 80 km/h, what speed is needed to make the same trip in 4.2 hours?

The volume \( V \) of a cone varies jointly as its height \( h \) and the square of its radius \( r \). If a cone with a height of 8 cm and radius of 2 cm has a volume of 33.5 cm³, what is the volume of a cone with a height of 6 cm and radius of 4 cm?