A can do a piece of work in 12 days, and B can do the same work in 15 days. With the help of C, they can finish the work in 5 days. How long will it take C to finish the work?
- A18 days
- B20 days
- C17 days
- D19 days
Solution & Step-by-step Explanation
Let the total work be the LCM of 12, 15, and 5, which is 60 units.
Efficiency of A =
12
60
=5 units/day
Efficiency of B =
15
60
=4 units/day
Combined efficiency of A, B, and C =
5
60
=12 units/day
Efficiency of C can be calculated as:
Efficiency of C=(Efficiency of A + B + C)−(Efficiency of A+Efficiency of B)
Efficiency of C=12−(5+4)=12−9=3 units/day
Time taken by C to complete the work alone:
Time=
Efficiency of C
Total Work
=
3
60
=20 days
Efficiency of A =
12
60
=5 units/day
Efficiency of B =
15
60
=4 units/day
Combined efficiency of A, B, and C =
5
60
=12 units/day
Efficiency of C can be calculated as:
Efficiency of C=(Efficiency of A + B + C)−(Efficiency of A+Efficiency of B)
Efficiency of C=12−(5+4)=12−9=3 units/day
Time taken by C to complete the work alone:
Time=
Efficiency of C
Total Work
=
3
60
=20 days