Question

P and R working together can finish a work in 10 days. If P works for 4 days then remaining work is completed in 15 days by R. Q is 2/3rd as efficient as R. Find the time taken by Q and R to do the same work if they are working together.​

Answer 1

Answer:

Q and R working together can finish the same work in 11 days

Step-by-step explanation:

Let the amount of work done by P in 1 day = 1/p

Amount of work done by Q in one day = 1/q

Amount of work done by R in one day  = 1/r

Since Q is 2/3 as efficient as R

Therefore

1/q = 2/3 × 1/r

Again

In 1 day P and R together can finish = 1/p + 1/r work

In 10 days P and R can finish = 10(1/p + 1/r) work

According to the question

10(1/p + 1/r) = 1

or 1/p + 1/r = 1/10  ..... (1)

In 4 days work done by P = 4/p

Remaining work = 1-(4/p)

This work is completed by R in 15 days

Therefore,

15/r = 1 - 4/p

or 15/r + 4/p = 1   .......... (2)

Multiplying eq (1) by 4 and subtracting from eq (2)

15/r - 4/r = 1 - 4/10

or, 11/r = 6/10

or, 1/r = 3/55

Let the number of days required by Q and R to finish the work is x

Then

x(1/q + 1/r) = 1

or, x(2/3r + 1/r) = 1

or, x/r(5/3) = 1

or, $x\times\frac{3}{55}\times \frac{5}{3} =1$

or, x = 11

Therefore, Q and R working together can finish the work in 11 days