Question

The ratio of boys to girls is 1 : 2. Two boys and two girls enter the room and the ratio is now 5 : 9. How many boys and girls were there originally?

Answer 1

Method 1)

Let the number of girls be x and number of boys be y.

The ratio of boys to girls is 1:2.

→ y/x = 1/2

→ x = 2y

Two boys and two girls were the room now the ratio becomes 5:9.

Number of girls = x + 2

Number of boys = y + 2

According to question,

→ (y + 2)/(x + 2) = 5/9

→ 9(y + 2) = 5(x + 2)

→ 9y + 18 = 5x + 10

As, x = 2y

→ 9y + 18 = 10y + 10

→ 10y - 9y = 18 - 10

→ y = 8

Substitute value of y in x

→ x = 2(8)

→ x = 16

•°• Number of girls = 16 and boys = 8.

$\rule{100}2$

Method 2)

Let the number of boys be x and girls be 2x.

Two boys and two girls enter the room and the ratio is now 5:9.

According to question,

→ (x + 2)/(2x + 2) = 5/9

→ 9(x + 2) = 5(2x + 2)

→ 9x + 18 = 10x + 10

→ 10x - 9x = 18 - 10

→ x = 8

Therefore,

Number of boys = 8

And number of girls = 2(8) = 16

Answer 2

Question :--- The ratio of boys to girls is 1 : 2. Two boys and two girls enter the room and the ratio is now 5 : 9. How many boys and girls were there originally ?

Solution :---

Let the number of boys and girls be x and 2x.

it has been said that now, when 2 boys and 2 girls enter the room, new ratio becomes = 5:9

So, according to Question :----

(x + 2) : (2x + 2) = 5:9

or,

→ (x+2)/(2x + 2) = 5/9

Cross -. Multiply ,

→ 9(x+2) = 5(2x+2)

→ 9x + 18 = 10x + 10

→ 18-10 = 10x - 9x

→ x = 8 ..

so ,

→ original boys = x = 8

→ original girls = 2x = 16 ..

Hence, their were 8 boys and 16 girls were in the room before..