CAT 2025 Question Paper | Quant Slot 1

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 11 : The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is

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Video Explanation

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Explanatory Answer

Let the initial number of students in the morning and afternoon shifts be \(13k\) and \(9k\).

After 21 students move from the morning shift to the afternoon shift:
Morning shift: \(13k-21\)
Afternoon shift: \(9k+21\)

Given ratio is \(19:14\):
\(\frac{13k-21}{9k+21}=\frac{19}{14}\)
\(14(13k-21)=19(9k+21)\)
\(182k-294=171k+399\)
\(k=63\)

\(13(63)-21=819-21=798\)
\(9(63)+21=567+21=588\)

The new students be \(3p\) and \(8p\).

The final ratio becomes \(5:4\):
\(\frac{798+3p}{588+8p}=\frac{5}{4}\)
\(4(798+3p)=5(588+8p)\)
\(3192+12p=2940+40p\)
\(p=\frac{252}{28}=9\)

Total New Students \(=3p+8p=11p\)
Total New Students \(=11\times9=99\)

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The answer is '99'

Choice 4 is the correct answer.

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