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CAT 2025 Slot 3 QA Question 20

Type-in-the-answer (no negative marking) · Arithmetic · Ratio, Proportion & Variation · Try it, then check the answer and solution below.

CAT 2025 Slot 3QAArithmetic • Ratio, Proportion & VariationModerate
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 Answer:
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Answer and solution

Answer: 272

📌 Core Concept
The problem involves ratios and requires setting up equations based on the given ratios before and after the transfer of coins. The key is to use variables to represent the initial quantities and solve for the unknown using algebraic manipulation.
🔢 Step-by-Step Solution
1
Let the initial number of coins in A and B be 17k and 7k respectively.
2
After transferring 108 coins:
A has 17k−10817k - 108 coins.
B has 7k+1087k + 108 coins.
3
Set up the ratio equation:
17k−1087k+108=3720\frac{17k - 108}{7k + 108} = \frac{37}{20}
4
Cross-multiply to solve for k:
20(17k−108)=37(7k+108)20(17k - 108) = 37(7k + 108) 340k−2160=259k+3996340k - 2160 = 259k + 3996
5
Simplify the equation:
81k=6156  ⟹  k=7681k = 6156 \implies k = 76
6
Calculate initial coins:
A: 17×76=129217 \times 76 = 1292
B: 7×76=5327 \times 76 = 532
7
After transferring 108

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