Question

102. In a school, the ratio of boys to girls is 4:5.
If 100 girls leave the school the ratio becomes
6:7. How many boys are there in the school?
a) 1400
b) 1500
c) 2400
d) 1200​

Answer 1

1400

let x = the multiplier

then

4x = original number of boys

and

5x = original number of girls

4x/5x-100=6/7

Cross multiply

7(4x) = 6(5x-100)

28x = 30x - 600

600 = 30x - 28x

600 = 2x

x = 600/2

x = 300 is the multiplier

then

4×300= 1200 boys

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Answer 2

Answer:

There are 1200 boys in the school.

Step-by-step explanation:

Given :-

• In a school, the ratio of boys to girls is 4 : 5.
• If 100 girls leave the school the ratio becomes 6 : 7.

To find :-

Number of boys in the school.

Solution :-

Let the number of boys be 4x and girls be 5x.

From girls ratio 100 left, so 5x - 100.

Then, the ratio is equal to 6 : 7.

• $\frac{4x}{5x-100}\;=\;\frac{6}{7}$

Cross multiplication :

• $4x(7)\;=\;6(5x-100)$

• $28x\;=\;30x-600$

• $2x\;=\;600$

• $x = \frac{600}{2}$

• $x = 300$

∴ Value of x is 300.

So, number of boys are 4(x) = 4(300) = 1200 boys.