At a workplace, one man alone can complete a work in 36 days. If the entire staff, i.e., 6 women and 4 men can complete the work in 6 days, how many days will one woman alone take to complete the entire work?
- A108
- B86
- C244
- D154
Solution & Step-by-step Explanation
Let the efficiency of 1 man be M and 1 woman be W.
The total work is completed by 1 man in 36 days:
Total Work=36×M=36M
The same total work is completed by 6 women and 4 men in 6 days:
Total Work=6×(6W+4M)=36W+24M
Equating both expressions for Total Work:
36M=36W+24M
36M−24M=36W
12M=36W⟹M=3W
Substitute M=3W into the total work equation:
Total Work=36M=36×(3W)=108W
Let D be the number of days taken by one woman alone to complete the work:
Work=1W×D
108W=1W×D⟹D=108 days
The total work is completed by 1 man in 36 days:
Total Work=36×M=36M
The same total work is completed by 6 women and 4 men in 6 days:
Total Work=6×(6W+4M)=36W+24M
Equating both expressions for Total Work:
36M=36W+24M
36M−24M=36W
12M=36W⟹M=3W
Substitute M=3W into the total work equation:
Total Work=36M=36×(3W)=108W
Let D be the number of days taken by one woman alone to complete the work:
Work=1W×D
108W=1W×D⟹D=108 days