P can complete a work in 15 days and Q in 24 days. They began the work together but Q left the work 2 days before its completion. In how many days was the work completed?
Time taken by P = 15 days
Time taken by Q = 24 days
Let Total work = LCM of 15 and 24 = 120 units
Efficiency of P = 120/15 = 8 units/day
Efficiency of Q = 120/24 = 5 units/day
Total Efficiency of P and Q = 8 + 5 = 13 units/day
Total work done by Q in 2 days = 5 × 2 = 10 units
Now New Total work = 120 + 10 = 130 units
∴ Total time taken to complete the work = 130/13 = 10 days