Question

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

• A. $13$
• B. $15$
• C. $17$
• D. $21$

Answer 1

The correct option is D $21$

Let the work done by B be $x$.

$\therefore$Work done by A $=2x$

Work done by A and B together in $14$ days $=1$

Work done by A and B together in $1$ day $=\frac{1}{14}$

$\Rightarrow$ Work done by A in $1$ day $+$ Work done by B in $1$ day $=\frac{1}{14}$

$x+2x=\frac{1}{14}$

$\Rightarrow 3x=\frac{1}{14}$

$\Rightarrow x=\frac{1}{42}$

Work done by B in $1$ day $=\frac{1}{42}$

$\therefore$ Work done by A in $1$ day $=\frac{1}{21}$

Hence, to finish the work, A require $21$ days.

Hence, A alone can finish the work in $21$ days.