A and B can do a work in 15 days and 30 days, respectively. They start working together, but A leaves after 3 days. How much time will B take to complete the remaining work?
- A28 days
- B21 days
- C24 days
- D32 days
Solution & Step-by-step Explanation
Let's find the total work using the LCM of 15 and 30.
Total Work=LCM(15,30)=30 units
Now, determine individual daily work efficiencies:
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
They work together for 3 days before A leaves:
Work completed in 3 days=3×3=9 units
Remaining work=30−9=21 units
Now, B completes the remaining work alone:
Time taken by B=
Efficiency of B
Remaining Work
=
1
21
=21 days
Total Work=LCM(15,30)=30 units
Now, determine individual daily work efficiencies:
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
They work together for 3 days before A leaves:
Work completed in 3 days=3×3=9 units
Remaining work=30−9=21 units
Now, B completes the remaining work alone:
Time taken by B=
Efficiency of B
Remaining Work
=
1
21
=21 days