CAT 2025 Slot 1 QA Question 19: 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. N

Question

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. N

Accepted Answer

Let the initial numbers of students in the morning and afternoon shifts be 13x and 9x.
$\dfrac{13x - 21}{9x + 21} = \dfrac{19}{14}$
$14(13x - 21) = 19(9x + 21)$
$182x - 294 = 171x + 399$
$11x = 693$
$x = 63$

Morning after transfer = $13 	imes 63 - 21 = 798$
Afternoon after transfer = $9 	imes 63