A can finish one-third of a work in 5 days, and B can finish 50% of the same work in 15 days. If they work together, then in how many days will they finish 50% of the work?
- A10
- B4
- C8
- D5
Solution & Step-by-step Explanation
Time taken by A to complete
3
1
of the work = 5 days.
Total time taken by A to complete the entire work (T
A
)=5×3=15 days.
Time taken by B to complete 50% (
2
1
) of the work = 15 days.
Total time taken by B to complete the entire work (T
B
)=15×2=30 days.
Let the total work be the LCM of 15 and 30, which is 30 units.
Efficiency of A=
15
30
=2 units/day
Efficiency of B=
30
30
=1 unit/day
Combined efficiency of A and B=2+1=3 units/day
We need to find the time taken to finish 50% of the work.
Work to be done=50% of 30=15 units
Time taken=
Combined efficiency
Work
=
3
15
=5 days.
3
1
of the work = 5 days.
Total time taken by A to complete the entire work (T
A
)=5×3=15 days.
Time taken by B to complete 50% (
2
1
) of the work = 15 days.
Total time taken by B to complete the entire work (T
B
)=15×2=30 days.
Let the total work be the LCM of 15 and 30, which is 30 units.
Efficiency of A=
15
30
=2 units/day
Efficiency of B=
30
30
=1 unit/day
Combined efficiency of A and B=2+1=3 units/day
We need to find the time taken to finish 50% of the work.
Work to be done=50% of 30=15 units
Time taken=
Combined efficiency
Work
=
3
15
=5 days.