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In a school the ratio of boys and girls is 4 : 5 respectively. When 100 girls leave the school the ratio becomes 6 : 7 respectively. How many boys are there in the school ?

11300
21500
31600
4None of these

Answer:- 1

Explanation:-

Solution:

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

\begin{aligned} = \frac{4 x}{5 x - 100} = \frac{6}{7} \\ \Rightarrow 28 x = 30 x - 600 \\ \Rightarrow 2 x = 600 \\ \Rightarrow x = 300. \\ ∴ Number of boys \\ = 4 \times 300 \\ = 1200. \end{aligned}

$\eqalign{ & {\text{ = }}\frac{{4x}}{{5x - 100}} = \frac{6}{7} \cr & \Rightarrow 28x = 30x - 600 \cr & \Rightarrow 2x = 600 \cr & \Rightarrow x = 300. \cr & \therefore {\text{Number of boys}} \cr & = 4 \times 300 \cr & = 1200. \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

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

\begin{aligned} = \frac{4 x}{5 x - 100} = \frac{6}{7} \\ \Rightarrow 28 x = 30 x - 600 \\ \Rightarrow 2 x = 600 \\ \Rightarrow x = 300. \\ ∴ Number of boys \\ = 4 \times 300 \\ = 1200. \end{aligned}

$\eqalign{ & {\text{ = }}\frac{{4x}}{{5x - 100}} = \frac{6}{7} \cr & \Rightarrow 28x = 30x - 600 \cr & \Rightarrow 2x = 600 \cr & \Rightarrow x = 300. \cr & \therefore {\text{Number of boys}} \cr & = 4 \times 300 \cr & = 1200. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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