Three men do as much work as 4 boys do in 21 days. In how many days will 9 men and 2 boys complete the same work?
- A8
- B7
- C6
- D11
Solution & Step-by-step Explanation
Let the efficiency of a man be M and a boy be B.
From the given statement ("Three men do as much work as 4 boys"):
3M=4B⟹M=
3
4
B
The total work can be computed using the capacity of 4 boys working for 21 days:
Total Work=4B×21=84B
We need to find the number of days (D) required by 9 men and 2 boys to complete the same work. Let's convert their combined efficiency into terms of B:
Combined Efficiency=9M+2B
Substitute M=
3
4
B:
Combined Efficiency=9(
3
4
B)+2B=12B+2B=14B
Now, using the formula Work=Efficiency×Time:
84B=14B×D
D=
14B
84B
=6days
From the given statement ("Three men do as much work as 4 boys"):
3M=4B⟹M=
3
4
B
The total work can be computed using the capacity of 4 boys working for 21 days:
Total Work=4B×21=84B
We need to find the number of days (D) required by 9 men and 2 boys to complete the same work. Let's convert their combined efficiency into terms of B:
Combined Efficiency=9M+2B
Substitute M=
3
4
B:
Combined Efficiency=9(
3
4
B)+2B=12B+2B=14B
Now, using the formula Work=Efficiency×Time:
84B=14B×D
D=
14B
84B
=6days