If 8 men and 10 women can do y units of work in 10 days; and 12 men and 21 women can do 2y units of work in 5 days, then what is the ratio of daily work done by a man to that of a woman?
Answer
Correct Answer : b ) 1:4
Explanation :It is given that,
8 men and 10 women can do y units of work in 10 days
12 men and 21 women can do 2y units of work in 5 days
Let the efficiency of 1 man and 1 woman be m and w respectively,
We know that,
Work done = efficiency x time taken
Total work = (8m + 10w) x 10 = y ---------1
Total work = (12m + 18w) x 5 = 2y ---------2
We need to equate the work by multiplying equation 1 by 2
2(8m + 10w) x 10 = 2y -----------3
From equation 2 and equation 3, we get
(8m + 10w) x 10 = (12m + 21w) x 5
80m + 100w = 60m + 105w
20m = 5w
4m = w
m : w = 1 : 4
The required ratio of daily work done by a man to that of a woman = 1 : 4
Hence, (b) is the correct option.
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