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

Entered answer:

✅ Correct Answer: 700

Let $S$ , $A$ , and $C$ be the number of students in Science, Arts, and Commerce respectively.

$S + A + C = 1500 \quad \cdots (1)$

$1100S + 1000A + 800C = 1550000 \quad \cdots (2)$

From $(1)$ :

$C = 1500 - S - A$

Substituting in $(2)$ :

$1100S + 1000A + 800(1500 - S - A) = 1550000$

$1100S + 1000A + 1200000 - 800S - 800A = 1550000$

$300S + 200A = 350000$

$3S + 2A = 3500 \quad \cdots (3)$

From $(3)$ :

$A = \dfrac{3500 - 3S}{2}$

Since the number of science students is not more than the number of arts students:

$S \leq A$

$S \leq \dfrac{3500 - 3S}{2}$

$2S \leq 3500 - 3S$

$5S \leq 3500$

$S \leq 700$

The maximum possible number of science students is $700$ .

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