7 men and 15 women can complete a piece of work in 15 days, and the same work…
2025
7 men and 15 women can complete a piece of work in 15 days, and the same work is completed by 18 men and 20 women in 8 days. If X men and 20 women can complete the work in 10 days, find X.
- A.
18
- B.
16
- C.
24
- D.
12
- E.
20
Attempted by 9 students.
Show answer & explanation
Correct answer: D
Concept
In work problems the total work is constant, so for any group (combined efficiency) x (days) = total work. Equating two scenarios that finish the same work gives the ratio of one man's efficiency to one woman's; once that ratio is fixed the total work can be written in efficiency units and any unknown number of workers found.
Application
Let one man's one-day efficiency be m and one woman's be w. Equate the first two scenarios (same total work): 15(7m + 15w) = 8(18m + 20w).
Expand: 105m + 225w = 144m + 160w, so 65w = 39m, giving m : w = 65 : 39 = 5 : 3.
Take w = 3 and m = 5 (any pair in 5 : 3). Total work = (7m + 15w) x 15 = (35 + 45) x 15 = 80 x 15 = 1200 units.
Third scenario: (X men + 20 women) work 10 days, so (5X + 20x3) x 10 = 1200, i.e. 5X + 60 = 120.
Solve: 5X = 60, so X = 12.
Cross-check
With X = 12, combined efficiency = 12x5 + 20x3 = 60 + 60 = 120 units/day; over 10 days that is 1200 units, exactly the total work. Consistent, so X = 12.