Question

The ratio of the number of men to the number of women in a sports club is 5:2.

Answer 1

Let the number of men and the number of women in the beginning be x and y

Now,$\sf \frac{x} {y} =\frac{5}{2} \\\\\sf=2x=5y \\\\\sf=x=\frac{5y}{2}$

Now, In 2nd case,

No. Of men=x-63 and no. Of women =y-12

Now,the ratio becomes$\frac{x-63}{y-12}=\frac{7}{4} \\\\\sf=4(x-63)=7(y-12) \\\\\sf=4x-252=7y-84 \\\\\sfPutting,\:x=\frac{5y}{2}\:in\: 4x-252=7y-84\:we\: get, \\\\\sf10y-252=7y-84 \\\\\sf=10y-7y=252-84 \\\\\sf=3y=168 \\\\\sf=y=56 \\\\\sf=\boxed{Y=56}$

Now,we have, 2x=5y

Putting the value of Y=56 in 2x=5y,we get,

$\sf 2x=5\:x\:56 \\\\\sfx=\frac{5\:x\:56}{2} \\\\\sfx=\frac{5\:x\: \cancel{56}\:\:28}{ \cancel{2}} \\\\\sf=x=5\: x\: 28 \\\\\sfx=140 \\\\\sf\boxed{x=140}$

Hence, the number of men was 140 and the no. of women was 56

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