Question

A works twice as fast as B. If B can complete a work in 12 days independently, then the number of days in which A and B can together finish the work is:
A. 4 days
B. 6 days
C. 8 days
D. 18 days

Answer 1

Hint: First we have given that B can complete a work in 12 days independently and the speed of A is twice the speed of B. It means if B can complete the work in 12 days, A can complete the same work in 6 days. By using this concept we solve the given question. First we find the work done by A and B in one day separately and then add the work done by both in one day.

Complete step-by-step answer:
We have given that B can complete a work in 12 days independently.
We have to find the number of days in which A and B can together finish the work.
The speed of A is twice the speed of B.
Now, as given B can complete a work in 12 days, so the work done by B in one day will be $\dfrac{1}{12}$
Now, the work done by A in one day will be
$\dfrac{2}{12}=\dfrac{1}{6}$ (as given A works twice as fast as B)
So, when A and B work together the work done by them in one day will be
$\begin{align}
  & \Rightarrow \dfrac{1}{12}+\dfrac{1}{6} \\
 & \Rightarrow \dfrac{1+2}{12} \\
 & \Rightarrow \dfrac{3}{12} \\
 & \Rightarrow \dfrac{1}{4} \\
\end{align}$
It means when A and B work together they complete the work in 4 days.
Option A is the correct answer.


Note:To solve such types of questions first we have to calculate the time taken by a single person to finish the work then we calculate the time taken by the person's work together. Don’t try to solve the question directly as given B can complete a work in 12 days independently, then both A and B can together finish the work in 6 days.