Problem Solving

P, Q R individually can complete a piece of work in 8, 12, 24 days. P and R start working together, After 4 days, R quits is replaced by Q. In how many days is work completed
A) 1 3/5 days
B) 5 3/5 days
C) 4 2/5 days
D) 5 1/5 days
E) None of these

OA
B

mitaliisrani wrote:P, Q R individually can complete a piece of work in 8, 12, 24 days. P and R start working together, After 4 days, R quits is replaced by Q. In how many days is work completed
A) 1 3/5 days
B) 5 3/5 days
C) 4 2/5 days
D) 5 1/5 days
E) None of these

OA
B

When the job is undefined, we can plug in our own number for the job. To make the math easy, we should choose a number that is a multiple of 8, 12 and 24.

Job = 24.
Rate of P = work/time = 24/8 = 3/day.
Rate of Q = work/time = 24/12 = 2/day.
Rate of R = work/time = 24/24 = 1/day.
Combined rate of P and R = 3+1 = 4/day.
Work completed by P and R in 4 days = rate * time = 4*4 = 16.
Remaining work = 24-16 = 8.
Combined rate of P and Q = 3+2 = 5/day.
Time to complete the remaining work = work/rate = 8/5.
Total time for job = 4 + 8/5 = 5 3/5 days.

The correct answer is B.

Time taken by P to finish the job = 8 days
Time taken by Q to finish the job = 12 days
Time taken by R to finish the job = 24 days

Time taken by P + R = 24x8/32 = 6 days to finish the job
Thus, in 4 days, P+Q finished 4/6 = 2/3 of the job

This job left to be done after 4 days = 1/3.

Time taken by P+R to finish 1 job = 96/20 = 24/5
Time taken by P+R to finish 1/3 job = 24/5 x 1/3 = 24/15 = 1 3/5 days

Thus, total time taken to finish the job = 4 + 1 3 3/5 = 5 3/5 days

P = 8
Q = 12
R = 24

So for the first four days P and R are working towards completing the project so let's see how much of the total project they complete in four days.

(PxR)/(P+R) = ??
(8x24)/(8+24) = 6

In 6 days P and R would complete the whole project but they only worked 4 days thus they completed 4/6 or 2/3 of the project leaving 1/3 left for P and Q.

We can start a tally of total project time. P and R worked 4 days so T = 4 + x, where x is the amount of time P and Q spent.

Let's see how long it would take P and Q to complete the whole project and then see how long it would take them to complete 1/3 of the project, the 1/3 that is left.

(PxQ)/(P+Q) = ??
(8x12)/(8+12) = (8x12)/20 = (8x3)/5 = 24/5

In 24/5 days P and Q could complete an entire project but only 1/3 is left so (1/3)(24/5) = 8/5.

It took P and Q 1 3/5 days to finish the remainder so T = 4 + 1 3/5 = 5 3/5

kmittal82 wrote:Time taken by P to finish the job = 8 days
Time taken by Q to finish the job = 12 days
Time taken by R to finish the job = 24 days

Time taken by P + R = 24x8/32 = 6 days to finish the job
Thus, in 4 days, P+Q finished 4/6 = 2/3 of the job

This job left to be done after 4 days = 1/3.

Time taken by P+R to finish 1 job = 96/20 = 24/5
Time taken by P+R to finish 1/3 job = 24/5 x 1/3 = 24/15 = 1 3/5 days

Thus, total time taken to finish the job = 4 + 1 3 3/5 = 5 3/5 days

@Mittal, u just that replaced Q & R !! But method used is fine...