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School Fee - Maximum Science Students

CAT 2025 Slot 3 · Quantitative Ability · Medium · Algebra

This is a medium Quantitative Ability question from the CAT 2025 Slot 3 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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 the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is

Answer

700

Explanation

Let S,A,CS, A, C be the number of science, arts, and commerce students. S+A+C=1500  ⟹  C=1500−S−AS + A + C = 1500 \implies C = 1500 - S - A. Total fee: 1100S+1000A+800C=1,550,0001100S + 1000A + 800C = 1,550,000. Divide by 100: 11S+10A+8C=1550011S + 10A + 8C = 15500. Substitute C=1500−S−AC = 1500 - S - A: 11S+10A+8(1500−S−A)=15500  ⟹  3S+2A=350011S + 10A + 8(1500 - S - A) = 15500 \implies 3S + 2A = 3500. We are given S≤AS \le A. To maximize SS, set A=SA = S: 3S+2S=3500  ⟹  5S=3500  ⟹  S=7003S + 2S = 3500 \implies 5S = 3500 \implies S = 700.

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