P, Q and R can do a work in 14, 42 and 56 days respectively. They started the work tpgether, but Q and R left 6 days and 8 days respectively, after starting the work. Remaining work was done by P alone. In how many days the remaining work was done by P ?

2 days

(P + Q + R) worked for 6 days and (P + R) worked for 2 days more. Remaining work is done by P .

Total work = Efficiency × Number of days

work done by (P + Q + R)  in 6 days = (12 + 4 + 3)R × 6
= 114R

Work done by   (P + R) in 2 days =  (12 + 3)R × 2=  30R

Remaining work = 168R - 114R - 30R  = 24R

Remaining work done by P in = \(\frac{24}{12}\) = 2 days