CAT 2023 Slot 3 QA Question 15: 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 c

Question

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 c

Accepted Answer

Let the weekly collections of A and B be $3k$ and $4k$ respectively.

A’s collection in 5 weeks is

$5 	imes 3k = 15k$

For this to be a multiple of 7, k must be a multiple of 7.

B’s collection in 3 weeks is

$3 	imes 4k = 12k$

For this to be a multiple of 24, k must be even.

So the least possi