CAT 2025 Slot 3 · Quant · Question 8

Let the original counts be 17k and 7k.

After the shift the counts are 17k-108 and 7k+108, and these are in the ratio 37:20.

Cross-multiplying, 20\left( 17k-108 \right)=37\left( 7k+108 \right), so 340k-2160=259k+3996.

That gives 81k=6156 and k=76.

So the boxes began with 17\times 76=1292 and 7\times 76=532 coins, a total of 1824.

After the 108 coins move, A holds 1292-108=1184 and B holds 532+108=640.

Shifting coins never changes the total, so an equal split means 912 coins each.

A must therefore give away a further 1184-912=272 coins.

Shortcut. The total is fixed at 1824 throughout, so the 1:1 target is known the moment k is found — half of 1824 is 912. No second ratio equation is needed.