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Question
Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?
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Solution
Let the number of days in which Mohan completes the work be x.
Number of days in which Manoj completes the work = x + 16
In one day, Mohan completes `1/x` parts of work.
In one day, Manoj completes `1/(x + 16)` parts of work.
It is given that they both can do the work in 15 days.
∴ `1/x + 1/(x + 16) = 1/15`
`(x + 16 + x)/(x(x + 16)) = 1/15`
`(2x + 16)/(x ^2 + 16x) = 1/15`
30x + 240 = x2 + 16x
x2 – 14x + 10x – 240 = 0
x2 – 24x + 10x – 240 = 0
x(x – 24) + 10(x – 24) = 0
(x – 24)(x + 10) = 0
x = 24, –10
Since, the number of days cannot be negative.
So, x = 24.
Thus, Mohan alone can complete the work in 24 days.
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