Let the number of men and the number of women in the beginning be x and y
Now,[tex]\sf \frac{x} {y} =\frac{5}{2} \\\\\sf
=2x=5y \\\\\sf
=x=\frac{5y}{2}[/tex]
Now, In 2nd case,
No. Of men=x-63 and no. Of women =y-12
Now,the ratio becomes[tex] \frac{x-63}{y-12}=\frac{7}{4} \\\\\sf
=4(x-63)=7(y-12) \\\\\sf
=4x-252=7y-84 \\\\\sf
Putting,\:x=\frac{5y}{2}\:in\: 4x-252=7y-84\:we\: get, \\\\\sf
10y-252=7y-84 \\\\\sf
=10y-7y=252-84 \\\\\sf
=3y=168 \\\\\sf
=y=56 \\\\\sf
=\boxed{Y=56}
[/tex]
Now,we have, 2x=5y
Putting the value of Y=56 in 2x=5y,we get,
[tex]\sf 2x=5\:x\:56 \\\\\sf
x=\frac{5\:x\:56}{2} \\\\\sf
x=\frac{5\:x\: \cancel{56}\:\:28}{ \cancel{2}} \\\\\sf
=x=5\: x\: 28 \\\\\sf
x=140 \\\\\sf
\boxed{x=140}
[/tex]
Hence, the number of men was 140 and the no. of women was 56
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