A piece of work can be done by Rams and Sham in 12 days, by Sham and Hart in 15 days and by Hart and Rams in 20 days. Rams alone will complete the work in how many days?
A. 35
B. 32
C. 30
D. 28
E. 25
Solution:
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
A. 35
B. 32
C. 30
D. 28
E. 25
Solution:
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
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