Question

When 10 girls left, the ratio of boys and girls became 2:1, and if afterwards 20 boys left, the ratio became 4:3. Find the sum of boys and girls?

• A. 120
• B. 180
• C. 100
• D. 150

Answer 1

Answer:

C. 100

Given:

The ratio of boys and girls when 10 girls left = 2 : 1

The ratio of boys and girls when 20 boys left = 4 : 3

Calculation:

Let there be x boys and y girls present

Then, $\frac{x}{(y - 10)}=\frac{2}{1}$

⇒ x = 2y - 20     -----(1)

Now, $\frac{(x - 20)}{(y - 10)}=4 : 3$

⇒ 3x - 60 = 4y - 40

⇒ 3x = 4y - 40 + 60

⇒ 3x = 4y + 20     -----(2)

Put the value of x from equation(1) in equation(2)

⇒ 3(2y - 20) = 4y + 20

⇒ 6y - 60 = 4y + 20

⇒ 6y - 4y = 20 + 60

⇒ 2y = 80

⇒ y = 40

Now, x = 2y - 20

⇒ x = 2 × 40 - 20

⇒ x = 80 - 20 = 60

Now, The sum of boys and girls = 40 + 60 = 100

∴ The sum of boys and girls is 100.