Question : The ratio of the number of boys to the number of girls in a school of 432 pupils is 5 : 4. When some new boys and girls are admitted, the number of boys increases by 12 and the ratio of boys to girls changes to 7 : 6. The number of new girls admitted is:
Option 1: 12
Option 2: 14
Option 3: 24
Option 4: 20
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Correct Answer: 24
Solution :
Given:
The ratio of the number of boys to the number of girls in a school of 432 pupils is 5 : 4.
Original number of boys in the school = $\frac{5}{9}× 432=240$
Original number of girls in the school = 432 – 240 = 192
Let the number of girls added be $x$.
According to the question,
$\frac{240+12}{192+x}=\frac{7}{6}$
⇒ $\frac{252}{192+x}=\frac{7}{6}$
⇒ $1344 + 7x = 1512$
⇒ $7x = 168$
$\therefore x=24$
Hence, the correct answer is 24.
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