CAT 2025 Question Paper | Quant Slot 3

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

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, to make this ratio 1:1, is

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Video Explanation

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Explanatory Answer

Let the initial number of coins in boxes A and B be \(17k\) and \(7k\), respectively.

After 108 coins are shifted from A to B:
Coins in A \(=17k-108\).
Coins in B \(=7k+108\).

Given the new ratio is \(37:20\):
\[ \frac{17k-108}{7k+108}=\frac{37}{20} \]
\[ 20(17k-108)=37(7k+108) \]
\[ 340k-2160=259k+3996 \]
\(81k=6156\Rightarrow k=76\).

Initial total coins:
\[ 17(76)+7(76)=24(76)=1824 \]
After the first transfer, box B has:
\[ 7(76)+108=640 \]

For equal numbers, each box must contain:
\[ \frac{1824}{2}=912 \]
Additional coins to shift from A to B:
\[ 912-640=272 \]

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The answer is '272'

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