A piece of work can be done by Ram and Shyam in 12 days, by Shyam and

Question

A piece of work can be done by Ram and Shyam in 12 days, by Shyam and Hari in 15 days and by Hari and Ram in 20 days. Ram alone will complete the work in how many days?

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

TestPrepUnlimited · Answer

Set R, S, and H as the respective rates.

Then we have R + S = 1/12, S + H = 1/15, H + R = 1/20.

We want to solve for R, we can eliminate S first by subtracting the first two equations with each other:

R - H = 1/12 - 1/15 = (15 - 12) / (12*15) = 3 / (12*15) = 1/60.

We also have R + H = 1/20.

Add these two equations to get: 2R = 1/60 + 1/20 = 1/60 + 3/60 = 4/60 = 1/15.

R = 1/30, so it would take R 30 days to complete the task alone.

Ans: C

exc4libur · Answer

(1/r+1/s)=1/12 - (1/s+1/h)=1/15
1/r-1/h=1/12-1/15
1/r-1/h=1/60;

1/r-1/h=1/60 + (1/r+1/h)=1/20
2/r=1/60+1/20
2/r=1/15
r=30

Ans (C)

freedom128 · Answer

Let r, s, h be the days required to complete a piece of works by Ram, Shyam, Hari, respectively.

(1/r + 1/s) -(1/s + 1/h) +(1/h + 1/r) = 1/12 -1/15 +1/20
1/r + 1/r = 2/r = 5/60 -4/60 +3/60 = 4/60
--> r =30 days

FINAL ANSWER IS (C)

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lacktutor · Answer

\frac{1}{r}+ \frac{1}{s}= \frac{1}{12} 
 
 \frac{1}{s} + \frac{1}{h}= \frac{1}{15} 
 
 \frac{1}{r} +\frac{1}{h} = \frac{1}{20}

—> adding all together: 
 2( \frac{1}{r}+ \frac{1}{s}+ \frac{1}{h}) = \frac{1}{12}+ \frac{1}{15}+\frac{1}{20}

\frac{1}{r}+ \frac{1}{s}+\frac{1}{h}= \frac{1}{10}

\frac{1}{r} = \frac{1}{10}–( \frac{1}{s}+ \frac{1}{h}) = \frac{1}{10}–\frac{1}{15} 
—>  \frac{1}{r} = \frac{1}{30}  
r = 30

The answer is C

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QuantMadeEasy · Answer

rate of (R+S) = 1/12 ----(i)
rate of (S+H) = 1/15 ---- (ii)
rate of (H+R) = 1/20 -----(iii)

rate of (R+S+H) = 1/10 ----(iv)
rate of R = 1/10 - 1/15 = 1/30

Ram alone can complete in 30 days

C is correct.

madgmat2019 · Answer

R+S=1/12........1
S+H=1/15........2
H+R=1/20........3

from 1-2+3....we get R can do the work in 30 days

OA:C

Jawad001 · Answer

Ram = R, Shyam = S, Hari =H
Rate of R + S = 1/12,
Rate of S + H = 1/15
Rate of H + R = 1/12
__________________________
2R + 2S + 2H = 1/12 + 1/15 + 1/20
 = 5 +4 + 3/60
 = 12/60
 = 1/5
R + S + H =1/10 
R = (R + S + H)- (S +H) = 1/10 -1/15 =6 – 4/60
 = 2/60
 =1/30
The number of days required by R to complete the work = 30 days(C)

Archit3110 · Answer

Total work
1/12+1/15+1/20= 12/60;1/5

Rams work; 
1/10-1/15= 1/30
30 days IMO C

A piece of work can be done by Ram and Shyam in 12 days, by Shyam and Hari in 15 days and by Hari and Ram in 20 days. Ram alone will complete the work in how many days?

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

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BrushMyQuant · Answer

Given that A piece of work can be done by Ram and Shyam in 12 days, by Shyam and Hari in 15 days and by Hari and Ram in 20 days. And we need to find Ram alone will complete the work in how many days?

Let Rate of Ram be R, Shyam be S and Hari be H.
We will be using   Rate * Time = Work done   formula.
Since work done is same so we will take work done as 1

A piece of work can be done by Ram and Shyam in 12 days 
=> Combined Rate = R + S
=> (R+ S) * 12 = 1
=>  R + S =  \frac{1}{12}   ...(1)

A piece of work can be done by Shyam and Hari in 15 days 
=> Combined Rate = S + H
=> (S+ H) * 15 = 1
=>  S + H =  \frac{1}{15}   ...(2)

A piece of work can be done by Hari and Ram in 20 days 
=> Combined Rate = H + R
=> (H+ R) * 20 = 1
=>  H + R =  \frac{1}{20}   ...(3)

(1) - (2) we get
R + S - (S + H) =  \frac{1}{12}  -  \frac{1}{15} 
=> R - H =  \frac{5}{60}  -  \frac{4}{60}  =  \frac{1}{60}  ...(4)

(3) + (4) we get
H + R + R - H =  \frac{1}{20}  +  \frac{1}{60}  =  \frac{3}{60}  +  \frac{1}{60}  =  \frac{4}{60}  =  \frac{1}{15} 
=> 2R =  \frac{1}{15} 
=> R =  \frac{1}{30}

Ram alone will complete the work in how many days 
=> R * Time = 1
=>  \frac{1}{30}  * Time = 1
=> Time = 30 days

So,  Answer will be C 
Hope it helps!

Watch the following video to learn How to Solve Work Rate Problems

https://www.youtube.com/watch?v=dRxzi_x3ZwY

vanshikaamittal · Answer

LCM (12,15,20)= 60
R+S= 60/12= 5
S+H= 50/15= 4
H+R= 60/20= 3

(R+S)- (S+H)+ (H+R)= 5-4+3
2R= 4
R=2

Time taken by R= 60/2= 30

is this the correct approach?

A piece of work can be done by Ram and Shyam in 12 days, by Shyam and

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