 QUESTION

# A is thrice as good as B and is therefore able to finish a job in 60 days less than that of B. In how many days can they together complete the job?(a) 20 days(b) $22\dfrac{1}{2}$ days(c) 25 days(d) 30 days

Hint: In this question, we will first find the difference in time taken by A and B taking smaller numbers. Then using the unitary method, solve the question for a difference of 60 days.

A is thrice as good as B. This means that, in completing an assigned job, A completes the job three times faster than that of B.
Let us consider that A completes a job in 1 day, then B will complete the same job in 3 days.
Here, B takes 3-1=2 days more than A to complete a job.
Here, we are given that A takes 60 days less than that of B to complete a job. That is, B takes 60 days more than A to complete a job.
Now, when B takes 2 days more than that of A to complete a job, he completes a job in = 3 days.
So, when B takes 1 day more than that of A to complete a job, he completes a job in = $\dfrac{3}{2}$ days.
Therefore, when B takes 60 days more than that of A to complete a job, he completes a job in = $\dfrac{3}{2}\times 60$ days
Dividing 60 by 2, we get,
$=90$ days.
Therefore, the fraction of the job done by B in one day =$\dfrac{1}{90}$.
Now, A takes 60 days less than that of B to complete a job.
Therefore, the number of days taken by A to complete a job = (90-60) days = 30 days.
Therefore, the fraction of the job done by A in one day $=\dfrac{1}{30}$.
Therefore, fraction of job done by A and B together in one day $=\dfrac{1}{30}+\dfrac{1}{90}$
Taking LCM, we get,
\begin{align} & =\dfrac{3+1}{90} \\ & =\dfrac{4}{90} \\ & =\dfrac{2}{45} \\ \end{align}
Hence, the number of days in which they together complete the job $=\dfrac{45}{2}=22\dfrac{1}{2}$ days.
Therefore, the correct answer is option (b).

Note: Alternative way to do this question is, we can take a number of days taken by A as $x$ and then find the job done in one day. Then use that in equation A=3B to solve the question.