Time and Work Practice Test 5 with solutions

Let the time taken by A and B be x and 2x respectively.
Work done by A and B in one day = $\frac{1}{\mathit{x}}+\frac{1}{2\mathit{x}}$
= $\frac{2+1}{2\mathit{x}}$ = $\frac{3}{2\mathit{x}}$
= $\frac{6}{2\mathit{x}}$ = $\frac{3}{\mathit{x}}$
Time taken by A and B be together = $\frac{2\mathit{x}}{3}$
Work done by A, B and C in one day
= $\frac{1}{\mathit{x}}+\frac{1}{2\mathit{x}}+\frac{3}{2\mathit{x}}$
= $\frac{2+1+3}{2\mathit{x}}$ = $\frac{6}{2\mathit{x}}$ = $\frac{3}{\mathit{x}}$
So, time taken by all the three of them = $\left(\frac{\mathit{x}}{3}\right)$ days
Now,
$\frac{\mathit{x}}{3}$ = 3
⇒ x = 9 days
So, time taken by A individually = 9 days
Time taken by B individually = 18 days
And time taken by C individually = $\frac{2}{3}\times 9$ = 6 days