Pervez and Sunny can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which Sunny was replaced by Ashu. If the work would be finished in next 4 days, find the number of days in which Ashu alone could complete the work.

Question: Pervez and Sunny can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which Sunny was replaced by Ashu. If the work would be finished in next 4 days, find the number of days in which Ashu alone could complete the work.

Solution:
Pervez can complete the work in 20 days
Sunny can complete the same job in 15 days
Let the total work = LCM of both
Therefore, the LCM of 20 and 15 is 60, that means total work = 60 units
Now, Pervez's one-day work efficiency = 60/20 = 3 units
Sunny's one-day work efficiency = 60/15 = 4 units
ATQ,
(Pervez + Sunny) together works for 6 days
That means (Pervez+Sunny) have done 7 × 6 = 42 units work in 6 days
Now, the remaining work will be 60 - 42 = 18 units, and it will finish in 4 days.
Now, Sunny is replaced with Ashu:
So, per days work required to be finished = 18 units / 4 days = 4.5 units
But, we know that Pervez's one-day work = 3 units, so Ashu's one-day work = 4.5 - 3 = 1.5 units
Therefore, Ashu alone can finish the total work in 60 units /1.5 days = 40 days