Find the difference between the number of girl students who choose IT and CSE stream.

Steps to Solve

1. Defining the Variables

Let the number of boys be denoted as $B$ and the number of girls as $G$.

2. Applying the Given Ratio

From the ratio of boys to girls ($B:G = 9:11$), we can express: $$ B = \frac{9}{20}x $$ $$ G = \frac{11}{20}x $$

Where $x$ is a common multiplier.

3. Setting Up the Equation for Difference

Given the difference between the number of girls and boys is 4000: $$ G - B = 4000 $$ Substituting the expressions for $G$ and $B$, we get: $$ \frac{11}{20}x - \frac{9}{20}x = 4000 $$

4. Solving for $x$

Simplify the equation: $$ \frac{2}{20}x = 4000 $$ Multiply by 20: $$ 2x = 80000 $$ Now divide by 2: $$ x = 40000 $$

5. Calculating the Number of Boys and Girls

Using $x$ to find $B$ and $G$: $$ B = \frac{9}{20} \times 40000 = 18000 $$ $$ G = \frac{11}{20} \times 40000 = 22000 $$

6. Finding the Count of Students in Each Stream

The number of boys choosing IT is 50% less than those choosing CSE: $$ \text{Boys in IT} = \frac{B}{2} = \frac{18000}{2} = 9000 $$ Thus, boys in CSE: $$ \text{Boys in CSE} = B - \text{Boys in IT} = 18000 - 9000 = 9000 $$

7. Applying the Ratio of CSE to IT Students

If the ratio of CSE to IT is $21:19$, let: $$ C = 21y, \quad I = 19y $$ So: $$ C + I = G $$ Substituting $C$ and $I$: $$ 21y + 19y = 22000 $$ Thus: $$ 40y = 22000 $$ Now solving for $y$: $$ y = 550 $$

8. Finding Total Students in Each Stream for Girls

Calculating the number of girls in each stream: $$ C (Girls) = 21y = 21 \times 550 = 11550 $$ $$ I (Girls) = 19y = 19 \times 550 = 10450 $$