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by sgr21 » Wed Dec 04, 2013 6:29 am
two men A & B can finish a piece ofwork in 12 days, A alone can finish the work in 48 days.however just before A & B start work B suffers an injury and works only at half of his previous efficiency.in how many days does A and injured B finish the work(if the answer is fraction round it off the next number ed 5 2/3 wil become 6 days)

A 20DAYS
B 18DAYS
C 16DAYS
D 14DAYS
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by Mathsbuddy » Wed Dec 04, 2013 7:46 am
Rate of work = number of tasks/time

Normally:
A = 1/48
and
A + B = 1/12
So B = 1/12 - 1/48 = 1/16

After injury:
B' = 1/16 * 1/2 = 1/32

A + B' = 1/48 + 1/32 = 5/96

If 5 tasks take 96 days then 1 task takes 96/5 = 19.2 days

Hence answer A) 20 DAYS

Is this right?
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by [email protected] » Wed Dec 04, 2013 1:22 pm
Hi sgr21,

Since we have two people working on a job together, this is a perfect opportunity to use the "work formula"

Work Formula = (AxB)/(A+B)

We're told:
A = 48 days to do a job
B = B days to do a job
Together = 12 days to do a job

So, let's plug in...

48B/(48+B) = 12

48B = 12(48+B)
4B = 48 + B
3B = 48
B = 16

Now we know that B takes 16 days to do the job.

We're told that B gets injured and now works at HALF his efficiency, so instead of taking 16 days, he takes 32 days.

So we have:
A = 48
B = 32

Plug in....

(48x32)/(48+32) = 96/5 = 19.2

Rounding to the nearest Day (as instructed), we get answer A

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by GMATGuruNY » Wed Dec 04, 2013 1:47 pm
sgr21 wrote:two men A & B can finish a piece ofwork in 12 days, A alone can finish the work in 48 days.however just before A & B start work B suffers an injury and works only at half of his previous efficiency.in how many days does A and injured B finish the work(if the answer is fraction round it off the next number ed 5 2/3 wil become 6 days)

A 20DAYS
B 18DAYS
C 16DAYS
D 14DAYS
Let the job = 96 units.

Combined rate for A and B together = w/t = 96/12 = 8 units per day.
Rate for A alone = w/t = 96/48 = 2 units per day.
Thus:
B's rate alone = (rate for A and B together) - (rate for A alone) = 8-2 = 6 units per day.
Since injured B works 1/2 as fast, rate for injured B = 3 units per day.

Combined rate for A and injured B = 2+3 = 5 units per day.
At a rate of 5 units per day, time to produce 96 units = w/r = 96/5 = 19 1/5 days.

The correct answer is A.
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by sgr21 » Thu Dec 05, 2013 1:15 am
THANKYOU GUYS A IS THE ANSWER
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