CAT 2025 Slot 1 · Quant · Question 11

CAT 2025 Slot 1 previous year question on Ratio and Proportion, with the answer and a step-by-step solution.

Ratio and ProportionArithmeticMultiple choiceMedium
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
  1. A
    110
  2. B
    88
  3. C
    121
  4. D
    99
Pick an option, then check.
Answer & solution

Answer: Option D

Take the original numbers as 13k and 9k. The transfer of 21 changes both:

\frac{13k-21}{9k+21}=\frac{19}{14}, so 14\left( 13k-21 \right)=19\left( 9k+21 \right), that is 182k-294=171k+399, giving 11k=693 and k=63.

So the shifts held 819 and 567, and after the transfer 798 and 588.

Now let the new students be 3m and 8m:

\frac{798+3m}{588+8m}=\frac{5}{4}, so 4\left( 798+3m \right)=5\left( 588+8m \right), that is 3192+12m=2940+40m, giving 28m=252 and m=9.

The number of new students is 3m+8m=11m=99.

Note the question asks for the total joining, not m.

More Ratio and Proportion questions

All Ratio and Proportion PYQs →

Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.

Practice timed →