Three man and 4 women can do a piece of work in 7 days, whereas 2 men and 1 women can do it in 14 days. Seven women will complete the same work in:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10 days
Concept
Since the work is same, we need to equate work in both cases which is given by :
M1D1 = M2D2
Here M1 and M2 represent number of men
D1 and D2 represent number of days.
Application
(3 men + 4 women) × 7 = (2 men + 1 women) × 14
(3 men + 4 women) = (2 men + 1 women) × 2
3 men + 4 women = 4 men + 2 women
2 women = men
(women ∶ men) = 1 : 2
Efficiency Ratio of (women ∶ men) = 1 ∶ 2
We know that
Total Work = Efficiency × Time
(3 men + 4 women) × 7 = (2 men + 1 women) × 14
(3 × 2 + 4 × 1) × 7 = (2 × 2 + 1 × 1) × 14 = 70
Total Work = 70
number of days taken to complete the work by 7 women = Total work/Efficiency
70 / (7 × 1)
10 days