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
Key idea: Eliminate commerce using the head-count equation, then apply the constraint science ≤ arts.
1. Let the counts be \( s, a, c \): \( s + a + c = 1500 \) and \( 1100s + 1000a + 800c = 1550000 \).
2. Subtract 800 times the first equation: \( 300s + 200a = 350000 \Rightarrow 3s + 2a = 3500 \).
3. Since \( a \ge s \): \( 3500 = 3s + 2a \ge 5s \Rightarrow s \le 700 \).
4. \( s = 700 \) gives \( a = 700 \) and \( c = 100 \), which is valid. Fee check: \( 770000 + 700000 + 80000 = 1550000 \).
Hence, the answer is 700.