Question

P, Q and R can do some work in 36 days. P and Q together do twice as much work as R alone and P and
R together can do thrice as much work as Q alone. Find the time taken by R to do the same work.​

Answer 1

Answer:

Solution of the given problem is shown below,

Let W denotes the whole given work.

According to given data,

(i) P, Q, & R together can complete the work W in 36 days.

(ii) After 4 days, P left and the rest of the work of W is done by Q & R together.

(iii) If P, Q & R all the 3 work equally, then

(iv) let D denotes the time (in days) in which the remaining work of W can be done by Q & R together.

(v) Let p, q & r denote the times (in days) in which P, Q & R alone can complete the work W respectively. Hence,

(vi) P, Q & R alone in 1 day can complete the amounts of work W/p, W/q & W/r respectively.

From (i) & (vi) we get following relation,

36*(W/p + W/q + W/r) = W

or 1/p + 1/q + 1/r = 1/36 …. (1a)

From (iii) & (vi) we get following relation,

W/p = W/q = W/r

or 1/p = 1/q = 1/r …. (1b)

From (1a) & (1b) we get,

1/p = 1/q = 1/r = 1/108 …. (1c)

From (ii), (iv) & (vi) we get following relation,

4*(W/p + W/q + W/r) + D*(W/q + W/r)= W

or 4*(1/p + 1/q + 1/r) + D*(1/q + 1/r)= 1

or 4*(1/36) + D*(2/108) = 1 [from (1a) & (1c)]

or D/54 = 1 - 1/9 = 8/9

or D = 8*54/9 = 48 (days) [Ans]