A and B can separately finish a work in 15 and 20 days, respectively. A starts the work and B joins him from the fifth day. How much time will it take to finish the complete work?
- A10
7
2
days - B11
7
3
days - C11 days
- D10 days
Solution & Step-by-step Explanation
Let the total work be the Least Common Multiple (LCM) of 15 and 20.
Total Work=LCM(15,20)=60 units
Now, find the daily efficiency of A and B:
Efficiency of A=
15
60
=4 units/day
Efficiency of B=
20
60
=3 units/day
A starts the work alone and works for the first 4 days (since B joins from the fifth day):
Work done by A in 4 days=4×4=16 units
Remaining work to be completed:
Remaining Work=60−16=44 units
From the fifth day onwards, both A and B work together:
Combined Efficiency of A+B=4+3=7 units/day
Time taken by both to finish the remaining work=
7
44
=6
7
2
days
Total time taken to finish the complete work:
Total Time=4 days+6
7
2
days=10
7
2
days
Total Work=LCM(15,20)=60 units
Now, find the daily efficiency of A and B:
Efficiency of A=
15
60
=4 units/day
Efficiency of B=
20
60
=3 units/day
A starts the work alone and works for the first 4 days (since B joins from the fifth day):
Work done by A in 4 days=4×4=16 units
Remaining work to be completed:
Remaining Work=60−16=44 units
From the fifth day onwards, both A and B work together:
Combined Efficiency of A+B=4+3=7 units/day
Time taken by both to finish the remaining work=
7
44
=6
7
2
days
Total time taken to finish the complete work:
Total Time=4 days+6
7
2
days=10
7
2
days