Arun completes 1/3 rd of a piece of work alone in 7/12th time taken by Roy to complete entire work alone. If they together can complete the work in 28 days, then how many days Arun working alone can complete the work?
Answers
Given : Arun completes 1/3 rd of a piece of work alone in 7/12th time taken by Roy to complete entire work alone. Together can complete the work in 28 days,
To find : in how many days Arun working alone can complete the work
Solution:
Let say Roy can complete the work alone in 12 D Days
7/12th time taken by Roy to complete entire work alone = (7/12)12D = 7D days
Arun completes 1/3 rd of a piece of work alone in 7D Days
=> Arun completes work alone in 7D/(1/3) = 21D Days
Roy 1 day work = 1/12D
Arun 1 Day work = 1/21D
Their total 1 Days work = 1/12D + 1/21D
= (7 + 4) /84D
= 11 /84D
11 /84D = 1/28
=> 11 = 3D
=> D = 11/3
Arun working alone can complete the work = 21D = 21 * 11 /3
= 77 Days
Arun working alone can complete the work in 77 Days
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