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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 the boys to girls changes to 7 : 6. The number of new girls admitted is:

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 the boys to girls changes to 7 : 6. The number of new girls admitted is: Correct Answer 24

Given:

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.

The ratio of boys to girls changes to 7 : 6.

Concept Used:

Properties of ratio.

Calculation:

Total number of students = 432

Ratio of boys to girls = 5 : 4

Number of boys = 5/9 × 432

⇒ 240

Number of girls = 432 – 240

⇒ 192

Let the number of new girls admitted be x,

(240 + 12)/(192 + x) = 7/6

⇒ 252 × 6 = 1344 + 7x

⇒ 7x = 1512 – 1344

⇒ x = 168/7

⇒ x = 24

∴ The number of new girls admitted is 24.

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Number of boys = 5/9 × 432 = 240

Number of girls = 432 – 240 = 192

Let the number of new girls admitted be x,

(240 + 12)/(192 + x) = 7/6

⇒ 252 = 7 unit

⇒ 1 Unit = 252/7 = 36 

⇒ 6 unit = 36 × 6 = 216

⇒ 192 + x = 216

⇒ x = 216 - 192

⇒ x = 24

∴ The number of new girls admitted is 24.

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