Question

The number of boys and girls in a class are in ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

Answer 1

Hint:
Let the number of boys be $7x$ and the number of girls be $5x$ as the ratio of boys and girls in a class is given as 7:5. Then, form the equation according to the given condition. Solve for $x$ to find the number of boys and number of girls and hence calculate the number of total students.

Complete step by step solution:
We are given that the ratio of boys and girls in a class is 7:5.
Therefore, let the number of boys be $7x$ (1)
And let number of girls be $5x$ (2)
Also, we are given that the number of boys is 8 more than the number of girls.
Then, according to question, we have
$7x = 5x + 8$
Taking $5x$ to LHS, we get
$
  7x - 5x = 8 \\
  2x = 8 \\
$
On dividing throughout by 2, we have,
$x = 4$
Substitute the value 2 for $x$ in equation (1) and equation (2).
Therefore, we have number of boys are $7\left( 4 \right) = 28$
And the number of girls is $5\left( 4 \right) = 20$.
There are 28 boys and 20 girls.
Total strength of class can be calculated by adding the number of boys and number girls.

Therefore, the total strength of class is $28 + 20 = 48$ students.

Note:
Ratio is used to compare things of the same kind. When two numbers are written in a ratio, it means that one number is expressed as the fraction of the other number.