Management Aptitude Test Sep 2013 Paper

(c) Efficiency = $\frac{1}{\mathrm{Time}\mathrm{taken}}$
Now, efficiency of A and C = 5x and 3x
As A taken 6 days less,
then
$\frac{1}{3\mathit{x}}-\frac{1}{5\mathit{x}}$ = 6
$\frac{5-3}{15\mathit{x}}$ = 6
$\frac{1}{\mathit{x}}=\frac{15\times 6}{2}$ ⇒ $\frac{1}{\mathit{x}}$ = 45
∴ Time taken by,
A = $\frac{1}{5\mathit{x}}=\frac{45}{5}$ = 9 days
and time taken by,
B = $\frac{1}{3\mathit{x}}=\frac{45}{3}$ =15 days
Ratio of number of days taken by B and C = 2 : 3
∴ Time taken by B = $\frac{2}{5}$ x 15 = 10 days
Now, B and C ’s one day work when worked together
= $\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}$ = $\frac{5}{30}=\frac{1}{6}$
Two days work of B and C = 2 x $\frac{1}{6}=\frac{1}{3}$
Remaining work = 1 - $\frac{1}{3}=\frac{2}{3}$
∴ Number of days taken by A to finish the work = $\frac{2}{3}$ x 9 = 6 days