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A started a work and left after working for 2 days. Then B did the rem

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Bunuel
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A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   28 Jan 2019, 05:07
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A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   28 Jan 2019, 06:10
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rate * time = work
let A is the rate of worker A, and B is the rate of worker B.

given:
2A + 9B = 3A + 6B
3B = A , B = A/3

to find A days:
2A + 9B = 2A + 9(A/3) = 2A + 3A = 5A; i.e: with rate of A, 5 days are needed to finish the work.

to find B days:
2A + 9B = 2(3B) + 9B = 6B + 9B = 15B; i.e: with rate of B, 15 days are needed to finish the work.

so A.
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A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   28 Jan 2019, 18:09
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A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days

let a=a's time to finish work alone
b=b's time to finish work alone
2/a+9/b=1
3/a+6/b=1
adding two equations,
5/a+15/b=2
plugging in choice A,
5/5+15/15=2 works
A=5 days and B=15 days
A
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   28 Jan 2019, 05:46
Bunuel wrote:
A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days


Let the Rate of A = RA & the Rate of B = RB

2RA + 9RB = 1..............1

3RA + 6RB = 1..............2

equation 1 & 2

2RA + 9RB = 3RA + 6RB.............RA = 3RB

From 3 in 1

6RB + 9RB = 1.........15RB =1...........RB = 1/15..........Time taken by B alone = 15 days

RA= 3 * 1/15 = 1/5..........Time taken by A alone = 5 days

Answer: A

P.S.: Many ways to solve 2 equation with 2 unknowns. I chose to find relationship between RA & RB less time for me than solving 2 equations simultaneously.
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   28 Jan 2019, 05:54
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Bunuel wrote:
A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days


Given :
If A would have worked for 3 days instead of 2 then B would have finished remaining work in 6 days instead of 9.

Hence work completed in 3 days by B is equal to work done by A in 1 day. (3B = 1A)

Total work = 2A + 9B = 2A + 3A = 5A
and 2A + 9B = 6B + 9B = 15B

IMO A
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   28 Jan 2019, 07:15
Bunuel wrote:
A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days



Rate of A = 2A and B = 9B
so work done is same
2a+9b=3a+6b
b=a/3

substitute value for a & b
we get
a= 2a+9a/3 = 15a/3 = 5a
b= 6b+9b = 15b

IMO A
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   21 Oct 2019, 12:04
Bunuel wrote:
A started a work and left after working for 2 days. Then B did the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them working alone, finish the whole work?

A. A = 5 days and B = 15 days
B. A = 7 days and B = 21 days
C. A = 8 days and B = 18 days
D. A = 4 days and B = 12 days
E. A = 15 days and B = 15 days


See the difference.
A worked for 2 days. B works 9 days to finish the remaining work.
A worked for 3 days. B works 6 days to finish the remaining work.

This gives us the fact that 1 day of work done by A is equal to 3 days of work by B.

Now let's say B didn't work at all.
A worked for 2 days. B works 9 days to finish the remaining work which is equal to 3 days of work done by A.
So A in total will take 5 days.

Only option A.
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink] New post   19 Dec 2023, 11:33
1) Lets assume work (w) = 1

2) Work = time*rate(w/days taken to complete) -> make an equation with the first one -> 1 = 2*1/a + 9*1/b

3) Use answer choice
- c) a = 8 / b = 18 -> 2/8 + 9/18 = 1/4 + 1/2 = 3/4 (not 1 so not correct)
- a) a = 5 / b = 15 -> 2/5 + 9/15 = (6+9)/15 = 1 (correct)
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Re: A started a work and left after working for 2 days. Then B did the rem [#permalink]
19 Dec 2023, 11:33
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