Question

P, Q and R together can complete a piece of work in 8 days. Q and R started working and P joined them after 6 days and it took them another 6 days to complete the work. Find the number of days which p alone can complete the work? * 15 days 12 days 18 days 14 days

Answer 1

No of days which p alone can complete the work = 12 days

Answer 2

P alone can do the work in 12 days.

Given: P, Q and R together can complete a piece of work in 8 days. Q and R started working and P joined them after 6 days and it took them another 6 days to complete the work.

To find: We have to find the number of days P alone can do the work.

Solution:

Let efficiency of P, Q and R is x, y, z.

Now P, Q and R together can complete a piece of work in 8 days.

So, we can write-

(x+y+z)×8 is the total work.

Q and R started working and P joined them after 6 days and it took them another 6 days to complete the work.

Thus we can write-

$(x+y+z)×8 = (y + z) \times 6 + (x + y + z) \times 6 \\ (x + y + z) \times 2 = 6y + 6z \\ 2x = 4(y + z) \\ \frac{x}{y + z} = \frac{2}{1}$

Thus total work will be (2+1)x×8=24x.

The efficiency of P is 2x.

Thus P alone can do the work in 24x/2x=12 days.