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A is twice as good as a 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. 13
B. 15
C. 17
D. 21

Answer Verified Verified
Hint: Take the number of days taken by B as $x$ and that of A as $\dfrac{x}{2}$ as it is mentioned in the question that A is twice as efficient as B. Then find the work completed by both in one day and equate their sum by $\dfrac{1}{42}$. Then find the number of days taken by B and after that find the number of days taken by A, which is the answer.

Complete step-by-step answer:
In the question, it is given that A is twice as good a workman as B, which means that A is twice as efficient as B. So, if we say that B takes $x$ amount of time to do a work, then A takes $\dfrac{x}{2}$ amount of time to do the same work.
Now, let us suppose that B takes $x$ days to complete a work, then we can say that in 1 day B completes $\dfrac{1}{x}$ amount of work.
Now, as we know that B takes $x$ days, then A will take $\dfrac{x}{2}$ days to complete the work. So, we can say that in 1 day A completes $\dfrac{2}{x}$ amount of work.
If A and B work together, then it takes them 14 days to complete the work. So, we can say that in 1 day A and B complete $\dfrac{1}{14}$ amount of work.
In terms of $x$, A and B complete $\left( \dfrac{1}{x}+\dfrac{2}{x} \right)$ or $\dfrac{3}{x}$ amount of work in 1 day. So, we can equate $\dfrac{3}{x}$ and $\dfrac{1}{14}$ as they represent the same quantities. So, we get,
$\begin{align}
  & \dfrac{3}{x}=\dfrac{1}{14} \\
 & \Rightarrow 3\times 14=x \\
 & \Rightarrow x=42 \\
\end{align}$
Hence, B takes 42 days to complete the work. As it is mentioned in the question that A is twice as efficient as B, so A takes $\dfrac{42}{2}=21$ days to complete the work.
Therefore, the correct option is D.

Note: Instead of taking $x$ as the number of days taken by B, we can take it as the number of days taken by A. In that case, B will take $2x$ days as A is twice as efficient as B. So, the equation will be, $\dfrac{1}{x}+\dfrac{1}{2x}=\dfrac{1}{14}$ and by simplifying, we get the direct value of the number of days taken by A, which is 21 days.