A, B and C can do a piece of work in 20 days, 10 days and 15 days respectively. They all started the work together but after 2 days B left the work and A left the work 3/2 days before the completion of work. Find the time in which work gets completed?

Correct option is A

Information given:
A, B and C can do a piece of work in 20 days, 10 days and 15 days respectively
They all started the work together but after 2 days B left the work and A left the work 3/2 days before the completion of work
Formulas Used:
Efficiency = total work/time taken to complete that work
Explanation:
Let the total work be 60 units (LCM of 20,10 and 15)
Efficiency of A= 3 units/day
Efficiency of B=6 units/day
Efficiency of C=4 units/day
B’s work in 2 days = 2 ×6 = 12 unit.
Total remaining work = 48 unit.
Let C works for x days.
Then, A will work for (x – 3/2) days.
ATQ,
x × 4 + (x – 3/2) × 3 = 48
7x = 52.5
x=7.5 days