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प्रश्न
The ratio of the number of boys to the number of girls in a school of 560 pupils is 5 : 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3 : 2.
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उत्तर
Ratio between boys and girls = 5 : 3
No. of pupils = 560
Sum of ratios = 5 + 3 = 8
∴ No of boys = `(5)/(8) xx 560` = 350
and No of girls = `(3)/(8) xx 560` = 210
No. of new boys admitted = 10
∴ Total number of boys = 350 + 10 = 360
Let the no. of girl admitted = x
∴ Total number of girls = 210 + x
Now according to the condition,
360 : 210 + x = 3 : 2
⇒ `(360)/(210 + x) = (3)/(2)`
⇒ 630 + 3x = 720
⇒ 3x = 720 – 630
⇒ 3x = 90
⇒ x = `(90)/(3)`
⇒ x = 30
∴ No of girls to be admitted = 30.
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