Question
Download Solution PDFA and B together take 5 days to do work, B and C take 7 days to do the same, and A and C take 4 days to do it. Who among these will take the least time to do it alone?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A and B take 5 days
B and C take 7 days
A and C take 4 days
Solution:
LCM(5, 7, 4) = 140 let total work be 140 unit
| Time | Work | Efficiency |
| 5 | 140 | 28 |
| 7 | 20 | |
| 4 | 35 |
The efficiency of A, B, C are
⇒ 2(A + B + C) = 28 + 20 + 35 = 83
⇒ A + B + C = 83/2 = 41.5
⇒ A = (A + B + C) - (B + C) = 41.5 - 20 = 21.5
By the same process
⇒ B = 41.5 - 35 = 6.5
⇒ C = 41.5 - 28 = 13.5
⇒ Time(A) = 140/21.5 = 6.51
⇒ Time(B) = 140/6.5 = 21.54
⇒ Time(C) = 140/13.5 = 10.37
A took the least time to complete the work. So, A is the fastest.
∴ A finishes fastest in 6.51 days.
Important Points We do not need to calculate the exact value we can find answer by approx value.
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