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X alone can do a piece of work in 15 days and Y alone can do it in 10

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Bunuel
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X alone can do a piece of work in 15 days and Y alone can do it in 10 [#permalink] New post   02 Dec 2020, 12:30
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Question Stats:

75% (02:01) correct 25% (02:57) wrong based on 63 sessions
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X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for $720. With the help of Z they finished it in 5 days. How much is paid to Z?

A. $360
B. $300
C. $240
D. $120
E. $100
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D
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X alone can do a piece of work in 15 days and Y alone can do it in 10 [#permalink] New post   02 Dec 2020, 18:29
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LCM (15,10) = 30 units

R T W
X 2 15 30
Y 3 10 30
Z 30

(X+Y+Z)xT=30
(2+3+Z)x5=30
Z=1

6 ---- 720$
1 ---- 120$

ANS: D
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Re: X alone can do a piece of work in 15 days and Y alone can do it in 10 [#permalink] New post   02 Dec 2020, 21:47
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Let the time taken by Z = a days

Work done by X in 1 day = 1/15

Work done by Y in 1 day = 1/10

Work done by Z in 1 day = 1/a

Work done by X, Y and Z in 1 day = 1/5

Therefore 1/15 + 1/10 + 1/a = 1/5

1/a = 1/5 - 1/10 - 1/15 = (6 - 3 - 2) / 30 = 1/30

Z alone finishes the work in 30 days

Ratio of Work done = 1/15 : 1/10 : 1/30 = 2 : 3 : 1

Amount paid to Z = (1 / 6) * 720 = 120


Option D

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Re: X alone can do a piece of work in 15 days and Y alone can do it in 10 [#permalink] New post   13 Nov 2022, 09:28
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Bunuel wrote:
X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for $720. With the help of Z they finished it in 5 days. How much is paid to Z?

A. $360
B. $300
C. $240
D. $120
E. $100


Let Z do the job in D days. Then, the rate of X, Y, and Z are 1/15, 1/10, and 1/D, respectively, and the combined rate is 1/5. Thus, we can write:

1/15 + 1/10 + 1/D = 1/5

30D(1/15 + 1/10 + 1/D) = 30D(1/5)

2D + 3D + 30 = 6D

30 = D

It follows that Z alone can do the job in 30 days, which means in 5 days, D can complete 5/30 = 1/6 of the job. Assuming each worker is paid in proportion to the amount of job they complete, Z should be paid 1/6 * 720 = $120.

Answer: D
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Re: X alone can do a piece of work in 15 days and Y alone can do it in 10 [#permalink]
13 Nov 2022, 09:28
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