TheCATExam
Sign in

XAT 2016 — QA & DI Question 16

Profit & LossEasy

Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in 60 : 40 ratio. The initial investment of Rs. 100,000 on infrastructure is borne entirely by ABC whereas the running cost of Rs. 400 per student is borne by XYZ. If each student pays Rs. 2000 for the program find the minimum number of students required to make the program profitable, assuming ABC wants to recover its investment in the very first year and the program has no seat limits.

Answer & solution

  • A

    63

  • B

    84

  • 105

  • D

    157

  • E

    167

Solution

Initial investment by ABC = 1,00,000

Let the total number of students be x.

Net profit from a student = 2000 – 400 = Rs. 1600

Net profit from ‘x’ students = 1600x

This will be divided between ABC and XYZ in the ratio of 60 : 40 i.e., 3 : 2.

∴ ABC will receive 1600x × 3/5

Hence, 1600x × 3/5 ≥ 1,00,000

⇒ x ≥ 104.2

∴ Minimum number of students should be 105.

Hence, option (c).

XAT 2016 QA & DI Q16: Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and X — Solution | TheCATExam