Averages , Ratio and Proportion Question 5 - CAT 2025
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:
Step-by-Step Explanation
- Determine the internal unit values:
Initial coin counts are A = 17x and B = 7x. Shifting 108 coins gives:
(17x − 108)/(7x + 108) = 37/20
20(17x − 108) = 37(7x + 108)
340x − 2160 = 259x + 3996
81x = 6156
⟹ x = 6156/81 = 76
- Find the aggregate pool metrics:
Total overall coins = (17 + 7) × 76 = 24 × 76 = 1824 coins
For the boxes to achieve a balanced 1 : 1 ratio, each box must contain exactly half of the total pool:
Target capacity per box = 1824/2 = 912 coins
- Compute the secondary transfer requirements:
Calculate box B's current coin count after the first shift:
Current count in B = 7(76) + 108 = 532 + 108 = 640 coins
Further coins required from A to B = 912 − 640 = 272 coins
Correct Answer: 272
💡 FundaMakers Tip:
In a closed-system transfer problem where the total number of items remains constant, the final 1 : 1 target equilibrium is always exactly half the total sum. Finding this total sum (1824) early on allows you to calculate the required shift using a simple subtraction step (912 − current), bypassing the need to solve another set of ratio equations.