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# A piece of work can be done by Ram and shyam in 12 days, By shyam Nad

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A piece of work can be done by Ram and shyam in 12 days, By shyam Nad [#permalink]

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03 Jun 2016, 19:00
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A piece of work can be done by Ram and shyam in 12 days, By shyam Nad hari in 15 days and by hari and ram in 20 days. Ram alone can complet the work in how much days ?

A . 30
B . 35
C . 25
D . 32
E . 28
[Reveal] Spoiler: OA

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Re: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad [#permalink]

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03 Jun 2016, 19:14
Top Contributor
anceer wrote:
A piece of work can be done by Ram and shyam in 12 days, By shyam Nad hari in 15 days and by hari and ram in 20 days. Ram alone can complet the work in how much days ?

A . 30
B . 35
C . 25
D . 32
E . 28

Rate*Time = Work
Since the work done is same throughout the question so we can take the work done as 1
Let Rate of Ram be R, Hari be H and Shaym be S

A piece of work can be done by Ram and shyam in 12 days
When Ram and Shyam will work together then their rate will be added. So combined rate will be R+S
(R+S)*12 = 1
R+S = 1/12 ...(1)

By shyam Nad hari in 15 days
Similarly
S+H = 1/15 ...(2)

hari and ram in 20 days
Similarly
H+R = 1/20 ...(3)

(2)-(3)
S+H - (H+R) = 1/15 - 1/20
=> S-R = 1/60 ..(4)

(1) - (4)
R + S - (S - R) = 1/12 - 1/60 = 4/60 = 1/15
2R = 1/15 => R = 1/30

Ram alone can complet the work in how much days ?
R * t = 1
t = 1/R = 1/ (1/30) = 30 days
Hope it helps!
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Re: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad [#permalink]

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03 Jun 2016, 19:16
1
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Expert's post
anceer wrote:
A piece of work can be done by Ram and shyam in 12 days, By shyam Nad hari in 15 days and by hari and ram in 20 days. Ram alone can complet the work in how much days ?

A . 30
B . 35
C . 25
D . 32
E . 28

We can calculate 1-day work of each pair and then find answer...
so $$\frac{1}{R} + \frac{1}{S} = \frac{1}{12}$$.........(i)
$$\frac{1}{S}+\frac{1}{H} = \frac{1}{15}$$.............(ii)
$$\frac{1}{H} + \frac{1}{R} = \frac{1}{20}$$.............(iii)

Now add (i) and (iii) and subtract (ii) from it...
(i) + (iii) - (ii)..................
$$\frac{1}{R} + \frac{1}{S} + \frac{1}{H} + (\frac{1}{R} + \frac{1}{S}- \frac{1}{H}) = \frac{1}{12} + \frac{1}{20} - \frac{1}{15}$$..................

$$\frac{1}{R} + \frac{1}{S} + \frac{1}{H} + \frac{1}{R} - \frac{1}{S} - \frac{1}{H} = \frac{1}{12} + \frac{1}{20} - \frac{1}{15}$$................

$$\frac{2}{R} = \frac{15+25-20}{300} = \frac{1}{15}$$..

$$R = 30$$

A
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Re: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad [#permalink]

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03 Jun 2016, 19:24
Let the individual rates for Ram, Shyam and Hari equal to r, s and h.
Given r+s = 12, s+h =15 and r+h = 20. Adding 3 equations 2(r+s+h) = 1/5 => r+s+h = 1/10, which means that all 3 can complete the same work in 10 days.
Now, individual work rate for Ram, r = (r+s+h) - (s+h) = 1/10 - 1/15 = 1/30.

Thus Ram can finish the work in 30 days. Hence A.

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Re: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad [#permalink]

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21 Aug 2017, 17:53
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Re: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad [#permalink]

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21 Aug 2017, 18:29
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We have Ram(R), Shyam(S) and Hari(H) who work on the piece of work.

R & S complete the piece of work in $$12(2^2 * 3)$$ days
S & H complete the piece of work in $$15(3*5)$$ days
H & R complete the piece of work in $$20(2^2 * 5)$$ days

Let the total piece of work be $$(2^2 * 3 * 5)60$$ units

Therefore the work done in a day by R & S is 5 units, the work done in a day by H & S is 4 units,
and the work done in a day by R & H is 3 units.

In total, they will do half of (3+4+5 = 12)units or 6 units of work in a day.
Therefore, Ram will be doing 2 units/day as Hari and Shyam do 4 units of work in a day.
So, to complete the 60 units of work, Ram will take 30 days(Option A)

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Re: A piece of work can be done by Ram and shyam in 12 days, By shyam Nad   [#permalink] 21 Aug 2017, 18:29
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