Question

Ratio of boys and girl is 4:5, when 100 girl left, the ratio becomes 6:7, find number of boys

1200

600

800

None of these

​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The number of Boys is 1200.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Ratio of boys to girls = 4 : 5

When 100 girls left, new ratio = 6 : 7

To find :

The number of Boys

Solution :

Consider the :

• Boys as 4x
• Girls as 5x

★ $\boxed{\sf{\frac{4x}{5x - 100} = \frac{6}{7}}}$

$\sf{\implies} \:\dfrac{4x}{5x - 100} = \dfrac{6}{7}$

$\sf{\implies} \:{7(4x)} = 6(5x - 100)$

$\sf{\implies} \:{28x} = 30x - 600$

$\sf{\implies} \:2x = 600$

$\sf{\implies} \:x = \dfrac{600}{2}$

$\sf{\implies} \:x = 300$

$\rule{300}{1.5}$

★ Value of 4x

$\sf{\implies} \:4 \times 300$

$\sf{\implies} \:1200$

Boys = 1200

$\therefore$ The number of Boys is 1200.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\sf{\implies} \:\dfrac{1200}{1500 - 100} = \dfrac{6}{7}$

$\sf{\implies} \:\dfrac{1200}{1400 } = \dfrac{6}{7}$

$\sf{\implies} \:\dfrac{1200 \div 200}{1400 \div 200} = \dfrac{6}{7}$

$\sf{\implies} \:\dfrac{6}{7} = \dfrac{6}{7}$

$\therefore$ The number of Boys is 1200.

Answer 2

Step-by-step explanation:

Let number of boys = 4N and number of girls = 5N

According to the question,

4N / (5N - 100) = 6 / 7

⇒ 28N = 6 ( 5N - 100 )

⇒ 28N = 30N - 600

⇒ 2N = 600

∴ N = 600 / 2 = 300

∴ Number of boys = 4N

= 4 x 300

= 1200

Hope it Helps !!!!