A and B together complete a piece of work in x days. If A alone completes the work in x + 3 days and B alone completes the piece of work in x + 12 days, what is the value of "x"?

Question: A and B together complete a piece of work in x days. If A alone completes the work in x + 3 days and B alone completes the piece of work in x + 12 days, what is the value of "x"?Solution:A's 1 day's work = 1/(x + 3) part B's 1 day's work = 1/(x + 12) partand (A + B)'s 1 day's work = 1/xATQ,1/(x + 3) + 1/(x + 12) = 1/x⇒ (x + 12 + x + 3)/(x + 3)(x + 12) = 1/x⇒ (2x + 15)/(x2 + 15x + 36) = 1/x⇒ 2x2 + 15x = x2 + 15x + 36⇒ 2x2 + 15x - x2 - 15x = 36⇒ x2 = 36∴ x = 6