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?

Answer 1

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.