CAT 2025 Slot 3 QA Question 4: In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all

Question

In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all

Accepted Answer

Let the numbers of science, arts and commerce students be $S$, $A$ and $C$ respectively.
$S + A + C = 1500$
$1100S + 1000A + 800C = 1550000$
Substitute $C = 1500 - S - A$ in the fee equation.
$1100S + 1000A + 800(1500 - S - A) = 1550000$
$300S + 200A = 350000$
$3S + 2A = 3500$
Given $S \leq A$. Sinc