Question

The boys and the girls in a school are in the ratio of $7:4$. The total strength of the school is $550$ . Find the number of girls and boys.

Answer 1

Hint: To solve this question we need to have the knowledge of ratio and exponents. The first step to calculate the question will be to consider an unknown variable$x$ . The ratio given to us is $7:4$, which means the total strength will be a sum of $7x$ and $4x$ which are the number of boys and girls respectively. We will equate the sum to $550$ , finding the value for $x$ and thereafter calculating the number of boys and girls.

Complete step by step answer:
The question asks us to find out the number of girls and boys in the class when the ratio of the total boys to girls is given as $7:4$ and the total strength of the school is stated as$550$. The first step is to consider an unknown variable$x$.

So the number of boys will be $7x$ and the total number of girls will be $4x$. Since the strength of the school is$550$. So mathematically the above explanation will be represented as:
$\Rightarrow 7x+4x=550$
Since the variables are the same, so on adding the coefficient of $x$ we get $11x$ which will be equal to $550$. On calculating it further we get the value for$x$, which is:
$\Rightarrow 11x=550$
Dividing the above expression by $11$ we will get:
$\Rightarrow x=\dfrac{550}{11}$
$\Rightarrow x=50$
Now to calculate the number of boys and girls, we will multiply $50$ with $7$ and $4$respectively. So on doing this we get:
The number of boys will be
$\Rightarrow 7\times 50$
$\Rightarrow 350$
The number of girls will be
$\Rightarrow 4\times 50$
$\Rightarrow 200$
$\therefore $ The number of girls and boys are $200$ and $350$ respectively.

Note: We can check whether the answer we got is correct or not. For this we will find the ratio of the number of boys to the number of girls. If the ratio comes out the same as $7:4$ and the total number of students results in $550$ then the answer is correct. So the ratio of the boys to girls is:
$\Rightarrow \dfrac{350}{200}$
On calculating the fraction we get:
$\Rightarrow \dfrac{7}{4}$
The ratio is the same as given in the question. Now we will check for the total number of students.
$\Rightarrow 350+200$
$\Rightarrow 550$
Since both the conditions are fulfilled, the answer we got is correct.