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'.

A can do work in x days

B can do work in (x + 16) days

In one day, A completes $\dfrac{1}{x}$ part of work

In one day, B completes $\dfrac{1}{x + 16}$ part of work

Given, both can do work in 15 days,

$\therefore \dfrac{1}{x} + \dfrac{1}{x + 16} = \dfrac{1}{15} \\[1em] \dfrac{x + 16 + x}{x(x + 16)} = \dfrac{1}{15} \\[1em] \dfrac{2x + 16}{x^2 + 16x} = \dfrac{1}{15} \\[1em] 15(2x + 16) = x^2 + 16x \\[1em] 30x + 240 = x^2+ 16x \\[1em] x^2 + 16x - 30x - 240 = 0 \\[1em] x^2 - 14x - 240 = 0 \\[1em] x^2 - 24x + 10x - 240 = 0 \\[1em] x(x - 24) + 10(x - 24) = 0 \\[1em] (x + 10)(x - 24) = 0 \\[1em] x + 10 = 0 \text{ or } x - 24 = 0 \\[1em] x = -10 \text{ or } x = 24.$

Since, no. of days cannot be negative,

∴ x ≠ -10.

Hence, x = 24 days.