Question : A certain factory employed 600 men and 400 women and the average wage was Rs. 2.55 per day. If a woman got 50 paise less than a man, the daily wages of a man and a woman would be _____.
Option 1: Man Rs. 2.75 and Woman Rs. 2.25
Option 2: Man Rs. 5.30 and Woman Rs. 2.50
Option 3: Man Rs. 2.50 and Woman Rs. 2.00
Option 4: Man Rs. 3.25 and Woman Rs. 2.75
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Correct Answer: Man Rs. 2.75 and Woman Rs. 2.25
Solution :
Given: The factory employed 600 men and 400 women and the average wage was Rs. 2.55 per day.
The total wages of 600 men and 400 women are (600 + 400) × 2.55 = Rs. 2550
Let a man's wage be $x$.
So, a woman's wage $=(x-\frac{50}{100}) = x-0.5$
So, the total wages of the 600 men and 400 women $=600x+400(x-0.5)$
According to the question,
$600x+400(x-0.5)=2550$
$⇒1000x=2750$
$\therefore x=2.75$
So, a man's wage is Rs. 2.75.
⇒ A woman's wage = (2.75 – 0.5) = Rs. 2.25
Hence, the correct answer is Man Rs. 2.75 and Woman Rs. 2.25.
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