A group of people is assigned a task of checking papers. They are supposed to continue working without rest, and checking 1 paper is considered as 1 piece of work. 2 men and 4 women together can do 125% of this piece of work in an hour. A man works twice as fast as a woman does. How much of the same work can 4 men and 2 women finish in an hour?
Solution
Correct Answer: Option D
Consider a woman alone can finish 1 piece of work in “x” hours.
Then, the work done by a woman in 1 hour = 1/x ----(1)
∴ Work done by a man in an hour = 2/x ----(2) (given)
∴ the work done by 2 men and 4 women in an hour = {2 × (2/x)} + {4 × (1/x)} = 8/x
Thus, 125% of a piece of work
= 1 1/4 pieces of work = (8/x) ----(3)
Now, work done by 4 men and 2 women in an hour
= {4 × (2/x)} + {2 × (1/x)} = 10/x ----(4)
∴ (8/x) ⇒ 5/4
∴ (10/x) ⇒ \(\frac{{\frac{{10}}{x}}}{{\frac{8}{x}}} \times \frac{5}{4}\; = \frac{{25}}{{16}}\)
Thus, 4 men and 2 women can finish 156.25% of a piece of work in an hour.
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