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A person x working alone can complete a work in 10 days. A person Y ..

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New post 18 Jun 2015, 17:16
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A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y leave the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25
[Reveal] Spoiler: OA

Last edited by anurag356 on 18 Jun 2015, 19:29, edited 1 time in total.

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New post 18 Jun 2015, 19:23
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anurag356 wrote:
A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25


I am assuming that the question is "...X and Y leave the work after 2 days?"

Rate of work of A = 1/10
Rate of work of B = 1/20
Rate of work of C = 1/30

Combined rate of work of all 3 = 1/10 + 1/20 + 1/30 = 11/60

In 2 days, the work they complete is Rate*Time = 11/60*2 = 22/60 of the work

We have (1 - 22/60 ) = 38/60 work leftover.

Time taken by C alone to complete the remaining work = Work/Rate = (38/60)/(1/30) = 19 days

Answer (A)
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A person x working alone can complete a work in 10 days. A person Y .. [#permalink]

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New post 18 Jun 2015, 20:36
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Expert's post
anurag356 wrote:
A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y leave the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25


ALTERNATE

Consider the Total work as Number of Units which is a common multiple of 10, 20 and 30 [to get away with the difficult calculation of Fractions]

Let, Total Work = 60 Units

X Finishes 60 Unit work in 10 days
i.e. Work done by X in a day = 60/10 = 6 Units

Y Finishes 60 Unit work in 20 days
i.e. Work done by Y in a day = 60/20 = 3 Units

Z Finishes 60 Unit work in 30 days
i.e. Work done by Z in a day = 60/30 = 2 Units

X and Y leave after two days while all start i.e. X, Y and Z work together for 2 days

Work done by X, Y and z in 2 days = 2*(6+3+2) = 22 Units

Work Remaining (to be finished by Z alone) = 60 - 22 = 38 Units

Time take by Z to finish 38 Units alone = 38/2 = 19 Days more

Answer: option
[Reveal] Spoiler:
A

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Re: A person x working alone can complete a work in 10 days. A person Y .. [#permalink]

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New post 27 Jun 2015, 00:53
anurag356 wrote:
A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y leave the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25


Alternate Nomenclature (but similar in way to Veritas' explanation)

Say, total unit of work = 1

X, working alone, can complete in 1 day = \(\frac{1}{10}\) amount of work
Y, working alone, can complete in 1 day = \(\frac{1}{20}\) amount of work
Z, working alone, can complete in 1 day = \(\frac{1}{30}\)amount of work

Therefore, all working together, in 1 day they complete = [\(\frac{1}{10}\) + \(\frac{1}{20}\)\(\) + \(\frac{1}{30}\)] amount of work.

For 2 days, all three of them worked together, therefore total work completed in 2 days = 2 * [\(\frac{1}{10}\)\(\) + \(\frac{1}{20}\) + \(\frac{1}{30}\)]

Let us suppose that after the 2nd day (i.e 3rd day onwards), when X and Y have left, Z takes 'd' number of days to complete the remaining work.

The final equation we get is:

\(2 * [\frac{1}{10} + \frac{1}{20} + \frac{1}{30}] + d * [\frac{1}{30}] = 1\) ---------------- (work completed + remaining work = total work)

Solving the equation, we get:

\(\frac{11}{30} + \frac{d}{30} = 1\)

d = 19 days ----- Answer.

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Re: A person x working alone can complete a work in 10 days. A person Y ..   [#permalink] 03 Jan 2018, 21:28
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