Question

A sports club has $130$ members. An increase of $10\%$ in the number of men and $20\%$ in the number of ladies brought up the membership to $148$. How many men and ladies were there originally?

• A. $90$ men, $40$ women
• B. $80$ men, $50$ women
• C. $60$ men, $70$ women
• D. $50$ men, $80$ women

Answer 1

Answer: (B)

$80$ men, $50$ women

Let the number of men be $x$ and women be $y$
Given, $x+y=130$ ....... $\left(1\right)$
And $1.1x+1.2y=148$ ....... $\left(2\right)$

Multiplying equation $\left(1\right)$ with $1.1$ we get,

$1.1x+1.1y=143$ ...... $\left(3\right)$

Subtracting equation $\left(3\right)$ from $\left(2\right)$, we get

$0.1y=5\Rightarrow y=50$

Substituting $y=50$ in the equation $\left(1\right)$, we get

$x+y=130\Rightarrow x=80$

Hence, the number of men $=80$ and number of women $=50$