P can do a work in 22 days. Q can do the same work in 16.5 days and R can do the same in 27.5 days.

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07 Nov 2017 Time and Work

P can do a work in 22 days. Q can do the same work in 16.5 days and R can do the same in 27.5 days. Q and R start the work and leave after 7.5 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 5 days
2) 5.5 days
3) 7 days
4) 6.0 days
5) 6.5 days
6) 8 days
7) 4 days
8) 4.5 days
9) 7.5 days
10) None of these

Solution

Amount of work done by Q and R in 7.5 days = 7.5*(1/16.5 + 1/27.5) = 7.5*((10+6)/165) = 120/165 = 8/11
Amount of work remaining after 7.5 days = 3/11

Amount of work done by P in 1 day = 1/22
So for 1/22 work P takes 1 day
Hence for 3/11 work P would take (1/(1/22))*3/11 = 6 days

Option 4)

Correct Option: 4 Best Solution (2)

Varun   7 years AGO

If it requires Y days to complete a work.
Then 1/Y work is done per day.
So,work done=
(1/16.5+1/27.5)×7.5 = .2727
Remaining work = x/22
No. of days = 22× .2727 = 6

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SAYAN CHATTERJEE   7 years AGO

Job left after the working of Q & R =Wx= 1-7.5*(1/27.5+1/7.5)
So, days needed to complete Wx amount of job by P = 22*Wx
= 6.
So, X=6.
Option 4.

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