Question

18. The ratio of number of boys to the number of girls in a school of 1430 students is
7: 6. If 26 new girls are admitted in the school, find how many new boys may be​

Answer 1

Correct Question:

The ratio of the number of boys to the number of girls in a school of 1430 students is 7:6. If 26 new girls are admitted in the school find how many new boys may be admitted so that the ratio of number of boys to the number of girls may change to 8:7.

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Given:

• Total number of student = 1430
• Ratio of no. of boys to no. of girls of 1430 students = 7:6

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To find:

• New boys admitted so the ratio may change to 8:7

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SoluTion:

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☯ Total number of student = 1430

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Let the number of boys be x.

So, number of girls = 1430 - x

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$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

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Ratio of no. of boys to no. of girls of 1430 students = 7:6

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Therefore,

$:\implies\sf \dfrac{x}{1430 - x} = \dfrac{7}{6}$

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$:\implies\sf 6x = 7(1430 - x)$

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$:\implies\sf 6x = 10010 - 7x$

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$:\implies\sf 6x + 7x = 10010$

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$:\implies\sf 13x = 10010$

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$:\implies\sf x = \cancel{ \dfrac{10010}{13}}$

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$:\implies{\underline{\boxed{\sf{\purple{x = 110}}}}}\;\bigstar$

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$\therefore$ No. of boys = 110

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So,

No. of girls,

$:\implies\sf 1430 - 110$

$:\implies\bf 660$

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If 26 new girls are admitted in the school then,

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No. of girls in school = 660 + 26 = 686

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☯ Let no. of new boys admitted be y.

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$\underline{\bigstar\:\boldsymbol{According\:to\:given\: condition\::}}$

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$:\implies\sf \dfrac{770 + y}{686} = \dfrac{8}{7}$

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$:\implies\sf 7(770 + y) = 8 \times 686$

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$:\implies\sf 5390 + 7y = 5488$

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$:\implies\sf 7y = 5488 - 5390$

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$:\implies\sf 7y = 98$

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$:\implies\sf y = \cancel{ \dfrac{98}{7}}$

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$:\implies{\underline{\boxed{\sf{\purple{y = 14}}}}}\;\bigstar$

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$\therefore$ Hence, 14 new boys admitted to maintain the ratio 8:7.