Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After mixing well, an equal volume is taken out from B and poured into A. If the ratio of alcohol and water in A is 15:4, then the volume, in litres, initially taken out from A, is [TITA]
CAT Averages & Mixtures questions (2023–2025) — actual Quant questions with solutions
15 real CAT Averages & Mixtures questions from CAT 2023 to CAT 2025, each with options, the verified answer and a step-by-step solution. Practice one topic at a
15 real CAT questions · CAT 2023–2025 · 1 Easy · 2 Medium
A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is
The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is ____
Average Problem
The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is _____
Milk and Water
A 300 litre container. Water x litres, rest milk. Remove 2x litres solution, refill water. Final solution 72% milk. Find x.
Averages + Equations
There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is ________ TITA
Interactive Quiz: Milk and Water Ratio
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:
A vessel contains an acid-water solution. After adding 2 litres water and then 15 litres acid, concentrations change from 50% to 80%. Find the original water:acid ratio.
In 2022, average bonus of first 30 employees was Rs. 40,000; last 30 was Rs. 60,000; first and last 10 combined was Rs. 50,000. In 2023, first 10 doubled, last 10 tripled. Find average bonus in 2023.
The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order remains unchanged. The new mean is 2 more than the middle number and the new difference between largest and smallest is 64. Find the largest original number.
A 300-litre container is partially filled with water, rest milk. Twice the water is removed, then refilled with water. Final mix is 72% milk. How much water was initially added?
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.
There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers is
A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is
A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing it with cocoa powder. The same process is repeated to form mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16:9, then the ratio of cocoa in mixture P to that in mixture Q is:
Every question here appeared in an actual CAT paper. For the full paper, open its page from the question's year and slot, or browse another topic from the list. Also on IIMking.com.