P, Q and R can individually do a work in 10, 12 and 15 days respectively. They start working together and P leaves after 2 days. Q left 3 days before completion of work. In how many days was the work completed?

Correct option is C

P, Q and R can individually do a work in 10, 12 and 15 days respectively. They start working together and P leaves after 2 days. Q left 3 days before completion of work. In how many days was the work completed?

Solution:​

Let the total work = LCM of (10, 12, 15) = 60 

Then the efficiency of P = 60/10 = 6 unit/day

The efficiency of Q = 60/12 = 5 unit/day

The efficiency of R = 60/15 = 4 unit/day

The work done by (P+Q+R) in 2 days = (6+5+4)$$\times$$2 = 30 unit 

The work one by Q in three days = 3 $$\times$$​  5 = 15 unit 

Then the Remaining work done  R and Q =  45/9 = 5 days 

Total days  = 5 + 2 = 7 days.