Question

7. The ratio of the number of boys to the number of girls in a school

of 672 students is 5:7. When some new boys and girls are admitted, the

number of girls increases by 8 and the ratio of boys to girls changes to 3:4.

Calculate the number of new boys admitted.




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Answer 1

Answer:

20

Number of boys admitted = 20

Step-by-step explanation:

Given:

>> Total Number of students = 672

>> Ratio before admission of new students = 5:7

>> Ratio after admission of new students = 3:4

>> Increase in number of girls was by 8.

To Find:-

Total Number boys admitted =?

Procedure:-

Total Number of students = 672

Total Ratio = 5 + 7 = 12

$\sf Number \ of \ boys = \dfrac{5}{12} \times 672.$

$\sf Number \ of \ boys = 5 \times 56$

$\sf Number \ of \ boys = 280$

$\sf Number \ of \ girls = \dfrac{7}{12} \times 672$

$\sf Number \ of \ girls = 7 \times 56$

$\sf Number \ of \ girls = 392$

After admission of new boys, the quantity becomes 280 + x , where 'x' denotes the new students.

And after admission of new girls , quantity becomes 392 + 8 = 400

Given that after admission the ratio of boys is to girls becomes 3:4 ..

Applying direct proportion:-

$\sf \implies \dfrac{280+x}{400}= \dfrac{3}{4}$

Cross multiplication:-

$\sf \implies (280 + x) \times (4)= (3) \times (400)$

$\sf \implies 4x + 1120 = 1120$

Subtraction 1120 from both the sides.

$\sf \implies 4x +1120 -1120 = 1200 - 1120$

$\sf \implies 4x = 80$

Divide both sides by 4:

$\sf \implies \dfrac{4x}{4}= \dfrac{80}{4}$

$\implies \sf x = 20$