Eight men can complete a work in 54 days. In how many days will 6 men and 12 boys complete the same work if one man works as much as 2 boys?
- A36
- B30
- C24
- D40
Solution & Step-by-step Explanation
Given the efficiency relationship:
1 Man=2 Boys⟹Efficiency ratio (M : B)=2:1
Let:
Efficiency of a man = 2 units/day
Efficiency of a boy = 1 unit/day
First, calculate the total work:
Total Work=8 Men×54 days=8×2×54=864 units
Now, find the combined efficiency of 6 men and 12 boys:
Combined Efficiency=(6×2)+(12×1)=12+12=24 units/day
The time required to complete the same work is:
Time=
Combined Efficiency
Total Work
=
24
864
=36 days
1 Man=2 Boys⟹Efficiency ratio (M : B)=2:1
Let:
Efficiency of a man = 2 units/day
Efficiency of a boy = 1 unit/day
First, calculate the total work:
Total Work=8 Men×54 days=8×2×54=864 units
Now, find the combined efficiency of 6 men and 12 boys:
Combined Efficiency=(6×2)+(12×1)=12+12=24 units/day
The time required to complete the same work is:
Time=
Combined Efficiency
Total Work
=
24
864
=36 days