CAT 2025 Slot 3 QA Question 8: 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,

Question

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,

Accepted Answer

Let the initial numbers of coins in boxes $A$ and $B$ be $17x$ and $7x$ respectively.
$\dfrac{17x - 108}{7x + 108} = \dfrac{37}{20}$
$20(17x - 108) = 37(7x + 108)$
$340x - 2160 = 259x + 3996$
$81x = 6156$
$x = 76$
After the first shift, box $A$ has $17 	imes 76 - 108 = 1184$ coins and box $B$ has $

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