Management Aptitude Test Dec 2013 Paper

(c) Let A, B and C independently completes a work in x, y and z days
∴ $\frac{5}{\mathit{x}}=\frac{4}{\mathit{y}}$
⇒ $\frac{1}{\mathit{x}}=\frac{4}{5}\times \frac{1}{\mathit{y}}$    ......(i)
Since, $\frac{37}{100}$ work is completed in 3 days by all of them.
∴ $\frac{63}{100}$ work will be completed in 7 days by A and B.
∴ $\frac{7}{\mathit{x}}+\frac{7}{\mathit{y}}=\frac{63}{100}$
⇒ $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{9}{100}$
⇒ $\frac{4}{5\mathit{y}}+\frac{1}{\mathit{y}}=\frac{9}{100}$
⇒ $\frac{9}{5\mathit{y}}=\frac{9}{100}$
⇒ y = 20
∴    x = 25
Also,
$\frac{3}{25}+\frac{3}{20}+\frac{3}{\mathit{z}}=\frac{37}{100}$
⇒ $\frac{3}{\mathit{z}}=\frac{37-12-15}{100}=\frac{1}{10}$
∴ z = 30 days
Hence, the fastest worker will complete the work in 30 days.