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Two men undertook to do a job for $1400 and decided to divide

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Two men undertook to do a job for $1400 and decided to divide  [#permalink]

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New post 04 Aug 2018, 07:36
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Difficulty:

  45% (medium)

Question Stats:

65% (03:23) correct 35% (02:58) wrong based on 43 sessions

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Two men undertook to do a job for $1400 and decided to divide the money as per their contribution.One of them alone can do the job in 7 days and other one in 8 days.With the assistance of a boy , they together completed the work in 3 days.How much money boy should get?
1) $300
2) $325
3) $275
4) $250
5) $225

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Re: Two men undertook to do a job for $1400 and decided to divide  [#permalink]

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New post 04 Aug 2018, 08:49
1
GMATbuster92 wrote:
Two men undertook to do a job for $1400 and decided to divide the money as per their contribution.One of them alone can do the job in 7 days and other one in 8 days.With the assistance of a boy , they together completed the work in 3 days.How much money boy should get?

Total cost = 1400

A can do the job in 7 days
A's 1 day work = 1/7

B can do the job in 8 days
B's 1 day work = 1/8

Along with C they finish the job in 3 days

C's part of the job in 3 days :
= 1 - Total job done by A and B in 3 days
= 1 - 3 * ( 1/7 + 1/8 )
= 1 - 3 * (15/56)
= 1 - 45/56
= 11/56

Therefore, C will get 11/56 of total cost = 1400 * 11/56 = 275

Hence, C.
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Two men undertook to do a job for $1400 and decided to divide  [#permalink]

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New post 04 Aug 2018, 09:14
2
GMATbuster92 wrote:
Two men undertook to do a job for $1400 and decided to divide the money as per their contribution.One of them alone can do the job in 7 days and other one in 8 days.With the assistance of a boy , they together completed the work in 3 days.How much money boy should get?
1) $300
2) $325
3) $275
4) $250
5) $225

If you do not see the "combined amount of work" approach, another approach is to find the boy's daily rate and multiply by the 3 days he worked to calculate the portion for which he is paid.

(1)The boy's daily work rate
Find the combined daily rate of the men and subtract that from combined rate of all three.

The combined rate of the two men is
\((\frac{1}{7} +\frac{1}{8})=\frac{15}{56}\)

If the boy joins the two men, the combined rate is \(\frac{1}{3}\). Thus rate of men + rate of boy, B
\((\frac{15}{56}+\frac{1}{B})=\frac{1}{3}\)

\(\frac{1}{B}=(\frac{1}{3}-\frac{15}{56})\)

\(\frac{1}{B}=(\frac{56}{168}-\frac{45}{168})\)

Boy's rate: \(\frac{1}{B}=\frac{11}{168}\)

(2) Amount of work the boy does in 3 days
\((\frac{11}{168}*3)=\frac{33}{168}\) of the work.

(3) Amount paid?
Paid proportionally, the boy gets
\((\frac{33}{168}*$1,400)=(\frac{33}{3}*$25)=(11*$25)=$275\)

Answer C
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Two men undertook to do a job for $1400 and decided to divide  [#permalink]

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New post 04 Aug 2018, 09:17
GMATbuster92 wrote:
Two men undertook to do a job for $1400 and decided to divide the money as per their contribution.One of them alone can do the job in 7 days and other one in 8 days.With the assistance of a boy , they together completed the work in 3 days.How much money boy should get?
1) $300
2) $325
3) $275
4) $250
5) $225


1-(3/7+3/8)=11/56
11/56*$1400=$275
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Two men undertook to do a job for $1400 and decided to divide &nbs [#permalink] 04 Aug 2018, 09:17
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Two men undertook to do a job for $1400 and decided to divide

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