Question

The number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. What is the total class strength ?
A. 48
B. 47
C. 46
D. 45

Answer 1

Hint: Here we are given the ratio of girls and boys. So, we assume boys and girls as 7x and 5x respectively and then make an equation from the given condition. And after solving that equation we will get the value of x.

Complete step-by-step answer:

As we know that the ratio of the number of boys and girls in the class is given as 7 : 5.
So, if the number of boys in a class were 7x.
Then the number of girls should be 5x. Because their ratio is given as 7 : 5.
So, the strength of the class will be = number of boys in class + number of girls in class = 7x + 5x = 12x.
Now, we know that it is given in the question that the number of boys is 8 more than the number of girls.
So,
7x – 5x = 8
$\Rightarrow$ 2x = 8
On dividing both sides of the above equation by 2, we get,
$\Rightarrow$ x = 4
So, the number of boys should be equal to 7x =7*4 = 28.
Number of girls will be equal to 5x = 5*4 = 20
And the strength of the class will be 12x = 12*4 = 48.
Hence, the correct option will be A.

Note: Whenever we come up with this type of where we are given the ratio of boys and girls then we assume the number of boys and girls in terms of a variable x. Like if the ratio is a : b then if the number of boys is ax then the number of girls should be bx. And after that we make an equation from the given condition like here boys are 8 more than girls. On solving this equation, we will get the value of x. And after putting the value of x in the number of boys and girls we will get the number of boys and girls in class. So, the total strength of the class will be the sum of that.