#### 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 works 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 = x^2 + 16x`

`x^2 - 14x - 240 = 0`

`x^2 - 24x + 10x - 240 = 0`

x(x - 24) + 10(x - 24) = 0

(x - 24) (x + 10) = 0

Since the number of days cannot be negative So x = 24

Thus Mohan alone can complete the work in 24 days

Is there an error in this question or solution?

Solution 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? Concept: Quadratic Equations.