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

Correct Answer: The maximum possible number of science students in the school is 700.

Step-by-Step Explanation:

Step 1: Define variables for the number of students in each stream

Let $S$ be the number of students in the Science stream.
Let $A$ be the number of students in the Arts stream.
Let $C$ be the number of students in the Commerce stream.

Step 2: Formulate the equations from the given problem

1. Total number of students is 1500:

$S+A+C=1500$

2. Total fee collected is Rs 15,50,000:

$1100S+1000A+800C=1550000$

3. We are also given the condition that the number of science students is not more than the number of arts students:

$S\le A$

Step 3: Simplify the fee equation

Divide the entire fee equation by 100:

$11S+10A+8C=15500$

Step 4: Eliminate variable $C$

From the total students equation, express $C$ in terms of $S$ and $A$:

$C=1500-S-A$

Substitute this into the simplified fee equation:

$11S+10A+8(1500-S-A)=15500$

$11S+10A+12000-8S-8A=15500$

$3S+2A+12000=15500$

$3S+2A=3500$

Step 5: Maximize $S$ using the given inequality

Express $A$ in terms of $S$:

$2A=3500-3S$

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

Using the condition $S\le A$:

$S\le \frac{3500-3S}{2}$

$2S\le 3500-3S$

$5S\le 3500$

$S\le 700$

Thus, the maximum possible number of Science students is 700.