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

Given

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

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To Find

• The number of boys in the school.

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Solution

Let the number of boys be '4x'

Number of girls would be '5x'

Now we know that when 100 girls leave the ratio becomes 6:7.

So let's solve the below equation step-by-step to find the number of boys in the school.

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

Step 1: Cross multiply.

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

⇒ $\sf 4x(7) = 6(5x-100)$

⇒ $\sf 28x = 30x - 600$

Step 2: Flip the equation.

⇒ $\sf 28x = 30x - 600$

⇒ $\sf 30x-600=28x$

Step 3: Add 600 to both sides of the equation.

⇒ $\sf 30x-600+600=28x+600$

⇒ $\sf 30x = 28x +600$

Step 4: Subtract 28 from both sides of the equation.

⇒ $\sf 30x-28x=28x+600-28x$

⇒ $\sf 2x=600$

Step 5: Divide 2 from both sides of the equation.

⇒ $\sf \dfrac{2x}{2} = \dfrac{600}{2}$

⇒ $\sf x = 300$

∴ The number of boys in the school are → 4x = 4(300) = 1200

∴ The answer is d) 1200.

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Answer 2

✪Question✪

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 ?

✪Understanding first✪

• Ratio of girls : Boys is 4:5 , when 100 girls left the school the ratio becomes 6:7 . So, find no. of boys

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✪Given✪

• Ratio of Boy's : Girls = 4 : 5
• When, 100 girls left the school ratio becomes = 6 : 7

✪Find✪

• No. of boys in the school

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✪Solution✪

• Let the No. of boys be 4x respectively
• Let the No. of girls be 5x respectively

Then,

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

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

$\sf \implies( 4x \times 7 )=( 5x \times 6 - 600)$

$\sf \implies 28x = 30x - 600$

$\sf \implies 600 = 30x - 28x$

$\sf \implies 600 = 2x$

$\sf \implies 2x = 600$

$\sf \implies x = \cancel \dfrac{600}{2} \rightarrow300$

$\sf {\huge \therefore} {\huge \N}o. \: of \: boys \: in \: the \: school \rightarrow4x \rightarrow4 \times 300 \rightarrow1200$

✪Answer✪

In a school, the ratio of boys to girls is 4:5.If 100 girls leave the school the ratio becomes6:7. How many boys are there in the school?

a) 1400

b) 1500

c) 2400

d) 1200 ✔

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