P alone can do a job in 18 days. P and Q working together can do it in 15 days. They started to work together.After 10 days Q left, and P alone has to complete the job. In how many more days can P complete the job?

$$ work done = efficiency \times time $$

P alone can do a job in 18 days

P and Q working together can do it in 15 days

work done = LCM( 18, 15 )

                    = 90

efficiency of P = $$ \frac{90}{18} = 5 $$

efficiency of P + Q = $$ \frac{90}{15} = 6 $$

therefore efficiency of Q = 6 - 5 = 1

P and Q work together for 10 days 

total work done for 10 days = $$ 10 \times 6 = 60 $$

remaining work = 90 - 60 = 30

let x be the days required to complete the  remaining job by P

$$ 30 = x \times 5 $$

solving x = 6 days