P can do a work in 46.5 days. Q can do the same work in 31 days and R can do the same in 77.5 days.

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01 Jun 2018 Time and Work

P can do a work in 46.5 days. Q can do the same work in 31 days and R can do the same in 77.5 days. Q and R start the work and leave after 15 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 20.0 days
2) 16 days
3) 17 days
4) 12 days
5) 13 days
6) 15 days
7) 14 days
8) 11 days
9) 18 days
10) None of these

Solution

Amount of work done by Q and R in 15 days = 15*(1/31 + 1/77.5) = 15((2.5+1)/77.5) = 52.5/77.5 = 21/31
Amount of work remaining after 15 days = 10/31

Amount of work done by P in 1 day = 1/46.5
So for 1/46.5 work P takes 1 day
Hence for 10/31 work P would take (1/(1/46.5))*10/31 = 15 days

Option 6)

Correct Option: 6 Best Solution (5)

Devendra Marghade   6 years AGO

1 days work of P=2/93, Q=1/31, R=2/155
So 15 days work of Q & R and X days work of P= 15*(1/31 + 2/155) + X*2/93 = 1
=> 21/31 + 2X/93 = 1
=> (63 + 2X) = 93
=> 2X=30 or X=15

Option 6)

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SAYAN CHATTERJEE   6 years AGO

Work by Q and R in 15 days is 15(1/31+1/77.5)= 0.677
So, the remaining job is 1-0.677 = 0.323.
So, the time reqd to finish the job bybP is 46.5*0.323 = 15 days.
Option 6.

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Titir Misra   6 years AGO

P's 1 day work = 1/46.5

Q's 1 day work = 1/31

R's 1 day work = 1/77.5

(Q+R)'s 1 day work = 1/31+1/77.5 =7/155

As Q and R work for 15 days, so

(Q+R)'s 15 day work = 15* 7/155 = 21/31

Amount of work left = 1-21/31 = 10/31

P finishes this remaining work alone, so

Time taken by P = 10/31 / 1/46.5
=15

which is the required answer

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Varun   6 years AGO

Work done by B in 1 day = 1/31
And by C = 1/77.5
So, in 15 days they do is (1/31+1/77.5)*15
= 0.67741
Remaining = 1-0.67741
= .322
So A, who works at 1/46.5 at a day will take
46.5*0.322 days to complete remaining work
= 15 days
= Option (6)

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Mukund Manohar   6 years AGO

15*(1/31 + 1/77.5) + X*(1/46.5) = 1
=> 35*15 / 775 + X/46.5 = 1
=> 525/775 + 10X/465 = 1
=> 50*X = 750
Value of X = 15 days

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