Consider the following data:

	Average marks in English	Average marks in Hindi
Girls	9	8
Boys	8	7
Overall average marks	8.8	x

What is the value of x in the above table?

The correct answer is 7.8.

Step 1: Understand the given data

From the table provided in the question, we have the following data for English and Hindi marks:

• Average marks in English for Girls = 9

• Average marks in English for Boys = 8

• Overall average marks in English = 8.8

• Average marks in Hindi for Girls = 8

• Average marks in Hindi for Boys = 7

• Overall average marks in Hindi = $x$

Step 2: Find the ratio of the number of Girls to Boys

Let $N_g$ be the number of girls and $N_b$ be the number of boys.

We can use the weighted average formula for English marks to find the ratio of Girls to Boys ($N_g:N_b$):

$\text{Overall average in English}=\frac{9\times N_g+8\times N_b}{N_g+N_b}$

Given that the overall average in English is 8.8:

$8.8=\frac{9N_g+8N_b}{N_g+N_b}$

Cross-multiplying both sides:

$8.8(N_g+N_b)=9N_g+8N_b$

$8.8N_g+8.8N_b=9N_g+8N_b$

Rearranging the terms to group $N_g$ and $N_b$:

$8.8N_b-8N_b=9N_g-8.8N_g$

$0.8N_b=0.2N_g$

$\frac{N_g}{N_b}=\frac{0.8}{0.2}=4$

This means that $N_g=4N_b$, or the ratio of Girls to Boys is $4:1$.

Step 3: Calculate the value of x (Overall average in Hindi)

Now, using the weighted average formula for Hindi marks with $N_g=4N_b$:

$x=\frac{8\times N_g+7\times N_b}{N_g+N_b}$

Substitute $N_g=4N_b$ into the equation:

$x=\frac{8\left(4N_b\right)+7N_b}{4N_b+N_b}$

$x=\frac{32N_b+7N_b}{5N_b}$

$x=\frac{39N_b}{5N_b}$

$x=\frac{39}{5}=7.8$

Hence, the value of $x$ in the table is 7.8.