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: The ratio of working of A to working of B is 2:1 which means that A works double the times than B. Suppose, if B takes 6 days to do a task, then A will do the same task in three days only. Using this concept, we will solve this question.

Complete step-by-step solution -
It is given in the question that A works twice as fast as B. Also, B takes 12 days to complete a task independently. So, we have to find the number of days required if A and B both work together to do the same task. We can write the ratio of working of A to working of B as 2:1. Which means that A works with double the speed of B. Now, in order to find the work done by both of them in 1 day, we will use the unitary method. So, unitary method is an approach in mathematics in which we find the value of 1 unit and then we will multiply it with the required quantity to get the desired result.
We know that B takes 12 days to complete the work independently, so it means that the work done by B in one day will be equal to $\dfrac{1}{12}$.
We also have the condition that, A works with double the speed of B. So, the work done by A in one day will be, $\dfrac{2\times 1}{12}=\dfrac{2}{12}=\dfrac{1}{6}$.
Now, if A and B both work together, then the work done in one day will be, $\dfrac{1}{12}+\dfrac{1}{6}=\dfrac{1+2}{12}=\dfrac{3}{12}=\dfrac{1}{4}$.
Therefore, if A and B will work together then the same task can be done in 4 days.
Hence, option (A) is the correct answer.

Note: The possible mistake that the students can make in this question is by directly solving the question as follows. If A takes 12 days to do the work, then it will take $\dfrac{12}{2}=6$ days if both A and B work together, which will give them the wrong answer. Hence, the students must read the question carefully in order to avoid any mistakes.