A and B together can complete a work in 15 days. If A, B and C working together can complete the same work in 10 days, then in how many days can C alone complete the same work?
- A28
- B30
- C35
- D20
Solution & Step-by-step Explanation
Let total work be LCM(15,10)=30 units.
Efficiency of A+B=
15
30
=2 units/day
Efficiency of A+B+C=
10
30
=3 units/day
Efficiency of C:
Efficiency of C=(Efficiency of A+B+C)−(Efficiency of A+B)
Efficiency of C=3−2=1 unit/day
Time taken by C alone to complete the work:
Time=
Efficiency of C
Total Work
=
1
30
=30 days
Efficiency of A+B=
15
30
=2 units/day
Efficiency of A+B+C=
10
30
=3 units/day
Efficiency of C:
Efficiency of C=(Efficiency of A+B+C)−(Efficiency of A+B)
Efficiency of C=3−2=1 unit/day
Time taken by C alone to complete the work:
Time=
Efficiency of C
Total Work
=
1
30
=30 days