Question

P,Q" and "R" can complete the whole work in "20" days."P],[" starts the wörk and works for ' "x'" days while "Q" and "R],[" completes the remaining "2/5" of the work in "14" days then "],[" find the value of "x"​

Answer 1

Answer:

The value of x is 28

Step-by-step explanation:

Let in one day P can do work = 1/p

In one day Q can do work= 1/q

In one day R can do work = 1/r

Then in one day P. Q, R will do = 1/p + 1/q + 1/r work

In 20 days they will do = 20(1/p + 1/q + 1/r) work

According to the question

20(1/p + 1/q + 1/r) = 1

or 1/p + 1/q + 1/r = 1/20   ............ (1)

In x days P completed = 3/5 work

Therefore,

x/p = 3/5                        .............(2)

In 14 days Q and R completed 2/5 work

Therefore, 14(1/q + 1/r) = 2/5

or, 1/q + 1/r = 1/35         ...............(3)

Subtraction eq (3) from eq (1)

1/p = 1/20 - 1/35 = 1/5(1/4 - 1/7)

or, 1/p = 3/140

putting this value in eq (2)

3x/140 = 3/5

or x = 140/5 = 28

Therefore, the value of x is 28