Question

A works twice as fast as B. If B can complete work in 12 days independently, then the number of days in which A and B can together finish the work is:
\[\begin{align}
  & \text{A}.\text{ 4 days} \\
 & \text{B}.\text{ 6 days} \\
 & \text{C}.\text{ 8 days} \\
 & \text{D}.\text{ 18 days} \\
\end{align}\]

Answer 1

Hint:At first, use the information, A is twice as fast as B to conclude that A takes six days to finish the work. Then find the amount of work done by A and B independently in 1 day. Then find the total amount of work done by A and B in 1 day and hence find the total number of days by dividing 1 by the amount of work done by both in 1 day to get the answer.

Complete step by step answer:
In the question, we are told that A works twice as fast as B. If B can complete a work in 12 days then we have to find the number of days in which A and B can together finish the work.
So, we know that B can complete the work in 12 days. As we are given that, A is twice as faster as B so we can say A can complete the work in $\dfrac{12}{2}\text{days}\Rightarrow \text{6 days}$
We know that B can complete the whole work in 12 days so we can say that B completes $\dfrac{1}{12}$ part of the work in 1 day.
We know that A can complete the whole work in 6 days, so we can say that A completes $\dfrac{1}{6}$ part of the work in 1 day.
If worked together A and B both can complete $\left( \dfrac{1}{12}+\dfrac{1}{6} \right)$ part of work $\Rightarrow \left( \dfrac{1+2}{12} \right)\Rightarrow \left( \dfrac{3}{12} \right)\Rightarrow \dfrac{1}{4}$ part of work in 1 day.
Thus, A and B can complete whole work in $1\times 4\Rightarrow 4\text{ days}$
Thus, the correct option is A.

Note:
In the question, students might be confused and think that A can complete the work in 24 days instead of 6 days which can make their answer wrong. Also, one should first find the amount of work done in 1 day by A and B independently to avoid any further mistakes in the solution.