John and Nick together can complete a work in 10 days. They plan to do the job in a different way. I

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24 Jul 2015 Time and work

John and Nick together can complete a work in 10 days. They plan to do the job in a different way. In first day John do it whereas Nick do it for the next 2 days and this pattern is repeated again and again. If they have to finish the work in 18 days, then in how many days the man who finish the work do this work alone.

OPtion

1) 12
2) 10
3) 15
4) 16
5) 18
6) 24
7) 21
8) 27
9) 30
10)20

Solution

Let John do it alone in x days and Nich alone in y days,
then according to first given condition
1/x + 1/y = 1/10 (1)
According to second condition
18/3 (1/x + 2/y) = 1
1/x + 2/y = 1/6 (2)
On solving (1) & (2) y = 15 & x = 30
So Nick will finish the work in 18 days & he complete it in 15 days
Option 3)

Correct Option: 3 Best Solution (3)

Devendra Marghade   9 years AGO

If John and Nick working alone completes the work in 'J' and 'N' days respectively, then
(1/J)+(1/N)=1/10 ---(i)
As their 3 days work will be (1/J)+(2/N) which is equal to 1/6 of the 18 days ,in which they have to complete the work.
So (1/J) +(2/N)=1/6 ---(ii)
From (i) & (ii), N=15, J=30
So John finishes who alone can complete the work in 15 days.
Answer option(3)

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Piyush Telang   9 years AGO

John takes 'J' days to complete the work alone and Nick takes 'N' days to complete the work alone.
Then 1 day's worth of work for John and Nick are 1/J and 1/N respectively.
--> When both work together simultaneously then the work is completed in 10 days.
=> 1/J + 1/N = 1/10
which means that one-tenth of work is completed in 1 day when both work together simultaneously.
--> When they work alternatively such that on 1st day John works and on 2nd and 3rd day Nick works, then the works is completed in 18 days and at last day Nick finishes the work.
=> 1/J + 2/N = 3 x ( 1/18 )
which means that when they work alternatively total of 3 days are covered and out of 18 days worth of work they complete one-sixth of work in 3 days.
--> So solving the 2 equations, we get N =15 days.
Thus, Nick takes 15 days alone to complete the work and John takes 30 days to complete the work alone.
As Nick finishes the work at the 18th day the answer is 15 days.

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ADITYA SARIPALLI   9 years AGO

let the rate of work done by John = r1
let the rate of work done by Nick = r2
let the total work needs to be done = w

=> 10(r1+r2) = w -------> (1)

At the same time if they do the work in batches of 3 days (John 1 day & Nick 2 days)
then to complete the work (w) it takes 18 days.
Moreover it would be 'Nick' who will be completing the last batch.

Thus for 1st batch (i.e w/6) it takes ...
=> (r1+2r2) = (w/6) -------> (2)

Thus from (1) & (2), we have

10(r1 + r2) = 6(r1 + 2r2)
=> 2r1 = r2 -------> (3)

from (1) & (3), we have

10(3r1) = w OR 10((3/2) * r2) = w
=> (w/r1) = 30 OR (w/r2) = 15

Therefore,
No Of days to complete the job if John works alone = (w/r1) = 30
No Of days to complete the job if Nick works alone = (w/r2) = 15


Thus ans = 15 days.

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