If 12 men or 20 women can do a work in 54 days, then in how many days can 9 men and 12 women together do the work?
- A38 days
- B32 days
- C40 days
- D35 days
Solution & Step-by-step Explanation
From the problem statement:
Work done by 12 men=Work done by 20 women
12M=20W⟹3M=5W⟹1M=
3
5
W
Now, we need to find the time taken by 9 men and 12 women working together. Let's convert everything into women:
9M+12W=9(
3
5
W)+12W=15W+12W=27W
Using the formula M
1
D
1
=M
2
D
2
:
20 women×54 days=27 women×D
2
D
2
=
27
20×54
=20×2=40 days
Work done by 12 men=Work done by 20 women
12M=20W⟹3M=5W⟹1M=
3
5
W
Now, we need to find the time taken by 9 men and 12 women working together. Let's convert everything into women:
9M+12W=9(
3
5
W)+12W=15W+12W=27W
Using the formula M
1
D
1
=M
2
D
2
:
20 women×54 days=27 women×D
2
D
2
=
27
20×54
=20×2=40 days