Correct Answer  Option 3 : 12.8 days
Given:
P can do a piece of work = 20 days
Q can do a piece of work = 24 days
R can do a piece of work = 30 days
After the next 4 days, P left and after the next 4 days R also left
Concept used:
Total work = LCM
Formula used:
Efficiency = Work/Time
Calculations:
Total work = LCM = 120
Person

Time

Total work

Efficiency

P

20 days

120

120/20 = 6

Q

24 days

120

120/24 = 5

R

30 days

120

120/30 = 4

Total efficiency of P, Q, and R = 15
In first 4 days’ work done by P, Q and R = 15 × 4 = 60
Remaining work = 120 – 60 = 60
Q + R efficiency = 5 + 4 = 9
P left and In next 4 days work done by Q and R = 9 × 4 = 36
Remaining work = 60 – 36 = 24
Now, R left and Time taken by Q to complete the remaining work = 24/5 = 4.8
Total time taken to complete the work = 4 + 4 + 4.8 = 12.8 days
∴ Total time taken to complete the work is 12.8 days