Answer

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**Hint:**Here, we will first calculate A’s one day work and B’s one day work by assuming A takes x days and B take 2x day, and equate them with one day work when both A and B do the same work together. Then solve the equation obtained to get the number of days taken by A to complete the work alone.

**Complete step by step answer:**

Given, A is twice good as B to complete the work.

Therefore, B takes twice the number of days taken by A to complete the work.

Let A take x days to complete the work, then according to question, B takes 2x days to complete the same work.

Also given that both A and B together complete the work in 14 days.

Work done in one day = Reciprocal of days taken to complete the total work

A’s one day work = $\dfrac{1}{x}$

B’s one day work = $\dfrac{1}{{2x}}$

(A + B)’s one day work = $\dfrac{1}{{14}}$

According to the question,

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

Solving equation,

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

\[ \Rightarrow \dfrac{3}{{2x}} = \dfrac{1}{{14}}\]

On cross-multiplying, we get

$2x = 42$

$ \Rightarrow x = \dfrac{{42}}{2} = 21$

Therefore, A takes 21 days to complete the work, and B takes 2x i.e. 2 × 21 = 42 days to complete the work.

Hence, the correct option is (D).

**Note:**

In this type of question, always calculate and compare one day's work by taking reciprocal of the total time taken to do the work. As if a particular work is done in x days and the work done in one day will be $\dfrac{1}{x}$ part of the total work. Never calculate by considering the number of days to complete the total work. And also after finding the unknown value, but that value in the equation formed as it must satisfy the equation.

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