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05 Jan 2020, 17:57
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
65% (02:30) correct
35%
(02:33)
wrong
based on 303
sessions
History
Date
Time
Result
Not Attempted Yet
40 men and 20 women together can complete a work in 12 days and ratio of efficiency of a man to a woman is 2:3, find how many men are required to complete half of the work in 7 days?
(A) 70
(B) 35
(C) 30
(D) 60
(E) 45
(A) 70
(B) 35
(C) 30
(D) 60
(E) 45
10 Jan 2020, 07:12
Kudos
Bookmarks
TheNightKing
Solution:
The total work completed can be represented as:
(40 * 2x * 12) + (20 * 3x * 12) = 960x + 720x = 1680x
So, half the work is 840x.
Since the rate of 1 man in 7 days is 2x * 7 = 14x, the number of men needed is:
840x/14x = 60
Alternate Solution:
Since the ratio of efficiency of a man to a woman is 2:3, 3 men will be equivalent to 2 women. Therefore, 40 men and 20 women are equivalent to 40 + 20*(3/2) = 40 + 30 = 70 men. Since the whole work is completed in 12 days by 40 men and 20 women (or equivalently, 70 men), half the work will be completed by the same team in 12/2 = 6 days. Therefore, one man will complete half of the work in 70 * 6 = 420 days. To complete it in 7 days instead of 6, we need 420/7 = 60 men.
Answer: D
