Question

A is twice as good a workman as B and together they can finish a piece of work in $12$ days. In how many days A alone can finish the work?

• A. $18$
• B. $27$
• C. $36$
• D. None of these

Answer 1

Answer: (A)

$18$

Given:

$A$ is twice as good a workman as $B$ and together they can finish a piece of work in $12$ days

Let the work done by $B$ be $x$.

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

Work done by $A$ and $B$ together in $12$ days $=1$

Work done by $A$ and $B$ together in $12$ days $=\frac{1}{12}$

$\Rightarrow$ Work done by $A$ in $1$ days + Work done by $B$ in $1$ day $=\frac{1}{12}$

$\Rightarrow x+2x=\frac{1}{12}$

$\Rightarrow 3x=\frac{1}{12}$

$\Rightarrow x=\frac{1}{36}$

$\therefore$ Work done by $A$ in $1$ day $=2x=2\times \frac{1}{36}=\frac{1}{18}$

Hence, $A$ to finish the work alone required $18$ dyas

$\therefore$ Option $A$ is correct.