A and B, working together, can complete a work in d days. Working alone, A takes (8 + d) days and B takes (18 + d ) days to complete the same work. A works for 4 days. The remaining work will be completed by B alone, in:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 24 days
We know,
A can do the work in (8 + d) days
B can do the same work in (18 + d) days
From this, d = (8 × 18)1/2 = 1441/2 = 12
So, A can do the work in (12 + 8) i.e 20 days & B can do the same work in (18 + 12) i.e 30 days.
Now, ATQ,
(A + B) can complete the work in 12 days.
So, taking LCM of A's work and B's work i.e 60, we get the total units of work to be done. From this, A's per day work as 3 units and B's per day work as 2 units.
Total work = 60 unit
Amount of work done by A in 4 days = 3 × 4 = 12 units
Units of work left = 60 - 12 = 48
No of days required by B to complete the work = 48 / 2 = 24 days