Question

in a school the ratio of the number of boys to the number of girls is 4:5. When 100 girls leave the school,the ratio becomes 6:7. Find the number of boys in the school.​

Answer 1

Answer:

there are 80 boys is the correct answer

Answer 2

Answer -

• There are 1200 boys in the school.

To find -

• The number of boys in the school.

Step-by-step explanation -

• Here, it is given that in a school, the ratio of the number of boys to the number of girls is 4 : 5.

So let -

• The number of boys be "4x".
• The number of girls be "5x".

After 100 girls leave the school,

• The number of girls become "5x - 100".

Given that -

• When 100 girls leave the school, the ratio of the number of boys to the number of girls becomes 6 : 7.

Therefore -

$: \longmapsto \: \sf 4x : 5x - 100 = 6 : 7$

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

$: \longmapsto \sf \: 6 \: (5x - 100) = 7 \: (4x)$

$: \longmapsto \sf \: 30x - 600 = 28x$

$: \longmapsto \sf \: 30x = 28x + 600$

$: \longmapsto \sf \: 30x - 28x = 600$

$: \longmapsto \sf \: 2x = 600$

$: \longmapsto \sf \: x = \cancel{\dfrac{600}{2}}$

$: \longmapsto \underline{ \boxed{\sf \: x = 300}}$

• The value of x is 300.

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Hence -

$\rm No. \:of \:boys = 4x = 4 \times 300 = 1200.$