Management Aptitude Test Sep 2013 Paper

(c) Let the common ratio be x. Since, pipe A takes 2x h to fill or to empty the tank. Pipe B takes 3x h to fill or to empty the tank. Pipe C takes 4x h to fill or to empty the tank. Now, Pipe A and B can fill the tank in 3 h ∴ = $\frac{1}{2x}+\frac{1}{3x}=\frac{1}{3}$= $\frac{3+2}{6x}=\frac{1}{3}$ x = $\frac{5\times 3}{6}=\frac{5}{2}$So, pipe A, B and C simultaneously take 5h, 7.5 h and 10 h to fill or to empty the tank. Now, by given condition, $\left(\frac{1}{5}+\frac{1}{7.5}-\frac{1}{10}\right)$ + $\left(\frac{1}{7.5}+\frac{1}{10}-\frac{1}{5}\right)$ + $\left(\frac{1}{10}+\frac{1}{5}-\frac{1}{7.5}\right)$ = $\left(\frac{6+4-3}{30}\right)$ + $\left(\frac{4+3-6}{30}\right)$ + $\left(\frac{3+6-4}{30}\right)$ = $\frac{7}{30}+\frac{1}{30}+\frac{5}{30}$ = $\frac{13}{30}=\frac{2}{5}$ Hence, after 3 h tank is $\frac{2}{5}$ filled