Management Aptitude Test 2016 Paper

(c) Let three pipes be A, B and C and time taken to fill the tank by pipes A, B and C be a, b and c hours, respectively.
According to the question,
b = a - 5 and b = c + 4
∴ a = b + 5 and c = b - 4
Now, $\frac{1}{\mathit{a}}+\frac{1}{\mathit{b}}=\frac{1}{\mathit{c}}$
⇒ $\frac{1}{\mathit{b}+5}+\frac{1}{\mathit{b}}=\frac{1}{\mathit{b}-4}$
⇒ $\frac{2\mathit{b}+5}{{\mathit{b}}^2+5\mathit{b}}=\frac{1}{\mathit{b}-4}$
⇒ 2${\mathit{b}}^2$ - 8b + 5b - 20 = ${\mathit{b}}^2$ + 5b
⇒ ${\mathit{b}}^2$ - 8b -20 = 0
∴ b = $\frac{8\pm \sqrt{{\left(8\right)}^2+4\times 20}}{2}$
= $\frac{8\pm \sqrt{64+80}}{2}$
= $\frac{8\pm \sqrt{144}}{2}$
= $\frac{8\pm 12}{2}$
= $\frac{8+12}{2}=\frac{20}{2}$ = 10 h
Hence, time required by first pipe = b + 5 = 10 + 5
= 15 h