P and Q together can complete the work in 40 days. They started working together

Q. P and Q together can complete the work in 40 days. They started working together, but after 25 days efficiency of P and Q both reduced by 62.5% and 33.33% respectively, so it will take 15 days more to finish the work. If after 25 days, Q leaves the job, then find in how many days remaining work completed by P alone, when he worked with twice of its efficiency at what he is working at that time.

A.35 days

B.28 days

C.30 days

D.70 days

E. None of these

Ans: 35 days

Sol:

Let the efficiencies be P and Q respectively
Now,
(P + Q) x 15 = 30 x (P x 3/8 + 2/3 x Q)
P + Q = 3P/4 + 4Q/3

P/4 = Q/3
P/Q = 4/3
Amount of work to be completed in rest 15 days
by P alone = (4 + 3) x 15 = 105
Efficiency of P, at which he works onwards 15
days = 4 x 3/8 x 2 = 3 units/day
Required time = 105/3 = 35 days
Hence answer is option A