Question

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

Answer 1

Step-by-step explanation:

let the original number of boys be x

x:2x=1:2

x+2:2x+2=5:9

9x+18=10x+10

x=8

2x=16

Answer 2

The number of boys is 8 and number of of girls is 16.

Step-by-step explanation:

Let the number of boys is x and that of girls is y.

Then, we have

$\frac{x}{y}=\frac{1}{2}\\\\y=2x...(i)$

Now, two girls and two boys enter the room. Then we have

$\frac{x+2}{y+2}=\frac{5}{9}$

Plugging y = 2x

$\frac{x+2}{2x+2}=\frac{5}{9}$

Solve the equation for x

9x + 18 = 10x + 10

10x - 9x = 18 - 10

x = 8

From equation (i)

y = 2 × 8

y = 16

Therefore, the number of boys is 8 and number of of girls is 16.

#Learn More:

The denominator of a fraction exceeds the numerator by 5. If the numerator is increased  by 9 then the fraction is increased by 1. Find the fraction

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