Question : 2 men and 1 woman can complete a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs. 180 per day, then a woman will get:
Option 1: Rs. 150
Option 2: Rs. 140
Option 3: Rs. 120
Option 4: Rs. 160
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Correct Answer: Rs. 120
Solution :
Given: 2 men and 1 woman can complete a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days and a man gets Rs. 180 per day.
Let work done by a man in a day = m units
Let work done by a woman in a day = w units
According to the question,
(2m + 1w) × 14 = (4w + 2m) × 8
⇒ 28m + 14w = 32w + 16m
⇒ 12m = 18w
⇒ 2m = 3w
So, 2 men's work is equivalent to 3 women's work.
A man gets Rs. 180 per day,
So, 2 men get = (180 × 2) = Rs. 360
⇒ 3 women will get Rs. 360.
So, 1 woman will get $(\frac{360}{3})$ = Rs. 120
Hence, the correct answer is Rs. 120.
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