CAT 2025 Slot 3 QA Q8 Ratio, Mixtures & Averages

Question 8 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.

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 that needs to be shifted further from A to B, to make this ratio 1:1, is

TITA: type in the answer. There are no options and no negative marking.

Answer: 272 Ratio, Mixtures & Averages TITA

Solution

Let \(A = 17k\), \(B = 7k\). Then \(\frac{17k - 108}{7k + 108} = \frac{37}{20}\).
\(340k - 2160 = 259k + 3996 \Rightarrow 81k = 6156 \Rightarrow k = 76\).
Total coins \(= 24 \times 76 = 1824\); A now has \(1292 - 108 = 1184\).
For 1:1 each box needs 912, so shift \(1184 - 912 = 272\).

Shortcut. Total is unchanged: \(24k\) and \(57m\) must match, so the total is a multiple of 456.