Question

A certain factory employed $600$ men and $400$ women and the average wage was Rs. $25.50$ per day. If a woman got Rs. $5$ less than a man, then what are their daily wages?

• A. Man : Rs.$25$; Woman : Rs.$20$
• B. Man : Rs.$27.50$; Woman : Rs.$22.50$
• C. Man : Rs.$30$; Woman : Rs.$25$
• D. Man : Rs.$32.50$; Woman : Rs.$27.50$

Answer 1

The correct option is B Man : Rs.$27.50$; Woman : Rs.$22.50$

Let the wage of the man be $x$

Given that the woman wage is Rs. $5$ less than the man.

Therefore, the wage of the woman is Rs. $x-5$

Given that the average wage of the $600$ men and the $400$ women is $25.5$

Therefore, $25.5=\frac{(600\times x)+\left(400\right(x-5\left)\right)}{600+400}$

$⟹25.5=\frac{600x+400x-2000}{1000}$

$⟹1000x-2000=1000\times 25.5$

$⟹1000x=25500+2000$

$⟹1000x=27500$

$⟹x=27.5$

Therefore, the wage of the man is Rs. $27.50$ and

the wage of the woman is Rs. $x-5=27.5-5=22.50$