Averages , Ratio and Proportion Question 4 - CAT 2025
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:
Step-by-Step Explanation
- Analyze the Shift Phase:
Let the initial morning shift count be 13k and afternoon shift count be 9k. Moving 21 students yields:
(13k − 21)/(9k + 21) = 19/14
14(13k − 21) = 19(9k + 21)
182k − 294 = 171k + 399
11k = 693
⟹ k = 63
Updated Morning base count = 13(63) − 21 = 819 − 21 = 798
Updated Afternoon base count = 9(63) + 21 = 567 + 21 = 588
- Analyze the Expansion Phase:
New students join the morning and afternoon shifts in the ratio 3 : 8, which we can represent as 3t and 8t:
(798 + 3t)/(588 + 8t) = 5/4
4(798 + 3t) = 5(588 + 8t)
3192 + 12t = 2940 + 40t
252 = 28t
⟹ t = 252/28 = 9
- Calculate the total count of new students:
Total new students = 3t + 8t = 11t = 11 × 9 = 99
Correct Option: D
💡 FundaMakers Tip:
Break multi-stage ratio adjustments into isolated phases. Calculate the absolute numbers at the end of the first phase before moving to the next. This prevents you from building overly long equations with multiple variables.