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?​

Answer 1

Given -

• Ratio of boys and girls = 7:5

• The number of boys is 8 more than the number of girls.

To find -

• Strength of the class

Solution -

In the question, we are provided with the ratio of boys and girls in a class and we need to find the strength of the class, for that, we will first take the common ratio, x after that, we will add 8, to the ratio of boys and then, we will put it equal to the ratio of girls, then we will find value of x, then we will solve the further question.

Let -

The common ratio be x

So -

7 = 7x

5 = 5x

Now -

We will make an equation, from that equation, we will find the value of x here.

→ 5x + 8 = 7x

→ 7x - 5x = 8 (by transposition method)

→ 2x = 8

→ x = 8/2

→ x = 4

Now -

We will find the number of boys and girls, by multiplying the obtained value of x, with the 7 & 5.

→ No. of boys = 7x = 7 × 4 = 28

→ No. of girls = 5x = 5 × 4 = 20

Total strength -

No. of boys + No. of girls

→ Total strength = 28 + 20

→ Total strength = 48

Therefore, the total strength of the class is 48.

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Answer 2

Answer:

Given :-

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

To Find :-

• What is the total class strength.

Solution :-

Let, the number of boys be 7x

And, the number of girls will be 5x

According to the question,

↦ $\sf 7x =\: 5x + 8$

↦ $\sf 7x - 5x =\: 8$

↦ $\sf 2x =\: 8$

↦ $\sf x =\: \dfrac{\cancel{8}}{\cancel{2}}$

➠ $\sf\bold{\green{x =\: 4}}$

Hence, the required number of boys and girls are :

➲ Number of boys :

⇒ $\sf 7x$

⇒ $\sf 7 \times 4$

➦ $\sf\bold{\pink{28}}$

And,

➲ Number of girls :

⇒ $\sf 5x$

⇒ $\sf 5 \times 20$

➦ $\sf\bold{\pink{20}}$

Now, we have to find the total class strength then,

$\implies \sf Total\: class\: strength =\: Number\: of\: boys\: +\: Number\: of\: girls$

$\implies \sf Total\: class\: strength =\: 28 + 20$

$\implies \sf\bold{\red{Total\: class\: strength =\: 48}}$

$\therefore$ The total class strength is 48 .