Question

p and q together can complete a job in 12 days. Q and R together can complete it in 15 days. P and R together complete in 18 days All three work together for 3 days and then R leaves. In how many days can p and q complete the remaining work?​

Answer 1

P + Q = 12

Q + R = 15

P + R = 18

Take LCM of these 180 (total work)

P + Q = 15

Q + R = 12

P + R = 10

Solving this three equations we get

Efficiency of P = 6.5 , Q = 8.5 , R = 3.5

All the three work together for 3 days & then R leaves , remaining work completed by P & Q in (X) days

(P + Q + R)*3 + (P + Q)*X = 180

(6.5 + 8.5 + 3.5)*3 + (6.5 + 8.5)*X = 180

55.5 + 15X = 180

15X = 124.5

X = 8.3 days