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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?
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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