#### Question

A can do a piece of work in ‘x’ days and B can do the same work in (x + 16) days. If both working together can do it in 15 days; calculate ‘x’.

#### Solution

Work done by A in one day = 1/x

Work done by B in one day = `1/(x + 16)`

Together A and B can do the work in 15 days. Therefore we have

`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 - 24)(x + 10) = 0

x = 24, -10

Since x cannnot be negative

Thus x = 24

Is there an error in this question or solution?

Solution A Can Do a Piece of Work in ‘X’ Days and B Can Do the Same Work in (X + 16) Days. If Both Working Together Can Do It in 15 Days; Calculate ‘X’. Concept: Quadratic Equations.