Question
Download Solution PDFRam and Ramesh can do a work in 12 days, Ramesh and Somesh in 15 days and Somesh and Ram in 10 days. If Ram, Ramesh and Somesh work together, in how many days will they complete the work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ram and Ramesh can do work together =12 days
Ramesh and Somesh can do work together = 15 days
Somesh and Ram can do work together = 10 days
Formula used:
Work = Efficiency × Time
Calculation:
Let the Ram, Ramesh, and Somesh can complete the work together in X days
One day work of Ramesh and Ram = \({1\over12}\)
One day work of Ramesh and Somesh = \({1\over15}\)
One day work of Somesh and Ram = \({1\over10}\)
One day work of all three = \({1\over12}+{1\over15}+{1\over10}\) = \({5+4+6\over60}={15\over60}={1\over4}\)
Working twice they can complete the work in = 4 days
They can complete the work = 8 days
∴ The required result will be 8 days.
Alternate MethodCalculation:
Ram and Ramesh = 12 days
Ramesh and Somesh = 15 days
Somesh and Ram = 10 days
LCM of (12,15, & 10) = 60 units
Efficiency of Ram and Ramesh = 60/12 = 5 units
Efficiency of Ramesh and Somesh = 60/15 = 4 units
Efficiency of Somesh and Ram = 60/10 = 6 units
Efficiency of 2(Ram, Ramesh & Somesh) = 15 units(5 + 4 + 6)
Total Efficiency of Ram, Ramesh & Somesh = (5 + 4 + 6)/2 = 7.5 units
Time taken by Ram, Ramesh, and Somesh together to complete the work:
Time = Total work / Total Efficiency
⇒ 60/7.5 = 8 days
∴ Ram, Ramesh, and Somesh together will complete the work in 8 days.
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