Raman can do a piece of work in half the time taken by Kapil.

Question

Raman can do a piece of work in half the time taken by Kapil. Sunil can do the same work in one-third of the time taken by Raman. All three of them work on it for 30 days after which Kapil leaves. Sunil and Raman complete the remaining work in 18 more days. How many days would it take for Raman alone to complete the total work?

A. 52
B. 138
C. 207
D. 312
E. 414
 
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findingmyself · Answer

Let Kapil take R Days to complete the work

Raman= \frac{R}{2}  
 Sunil= \frac{R}{6}  
 Total rate=  \frac{6}{R} + \frac{2}{R} + \frac{1}{R} = \frac{9}{R}  
 Work done is 30 days= Total rate*30= \frac{270}{R}  
 Work done by sunil and Raman in 18 more days= Rate of sunil and raman*18 
 = \frac{8}{R} *18= \frac{144}{R}  
 Total work done= \frac{414}{R}  
 Number of Days for Raman alone= Work/Rate of Raman 
 = \frac{414*R  *  2/R} =207 Days

Dereno · Answer

The ratio of times of R = (1/2)* K . Hence, the ratio of R : K = 1:2

S = (1/3)*R

S : R = 1:3

Combining both the ratios , we get S : R : K = 1: 3 : 2*3.

The new time ratio  S : R : K = 1: 3 : 6

Efficiency ratio =  inverse of time . Thus, S : R : K = 6: 2: 1.

All work for 30 days. So, the total work done = efficiency * days = (6+2+1)*30 = 9*30 =  270 units  of work is completed.

Then , Kapil leaves the site. And the rest of the work is completed by Raman and Sunil in 18 days.

(2+6)*18 = 8*18 =  144 units  of work.

Total work = 270 + 144 =  414 units of work .

Efficiency = Total work / time taken.

Time taken by Raman = ?

2 = 414 / time of Raman

Time of Raman = (414)/2 =  207 days.

Option C

Souradeep17 · Answer

let say Kapil take x days ,Raman takes x/2 days and Sunil takes x/6 days

1 day work of them will be 1/x , 2/x and 6/x 
total work 9/x 
in 30 days work done 270/x
Then kapil left and they complete the remaining work in 18 days

8/x*18=144/x

Total work=270/x+144/x=414/x
for Raman to complete this work alone it would take= 
total work/raman's 1 day work=(414/x) / (2/x)
414/2=207. it should option C

Raman can do a piece of work in half the time taken by Kapil.

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Raman can do a piece of work in half the time taken by Kapil.

Prep Toolkit

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