Question

$A$ is twice as fast as workman as $B$ and together they finish a piece of work in 14 days. In how many days can $A$ alone finish the work?

• A. $18$ days
• B. $21$ days
• C. $24$ days
• D. $27$ days

Answer 1

The correct option is B $21$ days

If $B$ finishes the work in $x$ days, then $A$ finishes the work in $\frac{x}{2}$ days.

$\Rightarrow B$'s one day's work $=\frac{1}{x}$

and $A$'s one day's work $=\frac{2}{x}$

Given $\frac{1}{x}+\frac{2}{x}=\frac{1}{14}\Rightarrow \frac{3}{x}=\frac{1}{14}$

$\Rightarrow x=14\times 3=42$ days

$\therefore A$ alone can finish the work in $\frac{42}{2}=21$ days.