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15 Sep 2025, 00:39
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:54) correct
37%
(02:55)
wrong
based on 101
sessions
History
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Not Attempted Yet
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
A. 52
B. 138
C. 207
D. 312
E. 414
15 Sep 2025, 10:23
Kudos
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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
=\(\frac{414*R[}{fraction]\)*\([fraction]2/R}\)=207 Days
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
=\(\frac{414*R[}{fraction]\)*\([fraction]2/R}\)=207 Days
15 Sep 2025, 10:48
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Bunuel
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
