Question

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A. 5
B. $ 5\dfrac{1}{2} $
C. 6
D. 8

Answer 1

Hint: To solve this question first we will find the efficiency of both A and B and calculate the total work by taking the LCM of time taken by both of them to complete the work. Then we calculate the remaining work and calculate the number of days by using the efficiency of A.

Complete step by step answer:
We have been given that A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job.
We have to find the number of days A alone can finish the remaining work.
Now, first, we calculate the total work by taking the LCM of 18 and 15.
So, we have
 $ \begin{align}
  & 18=3\times 3\times 2 \\
 & 15=3\times 5 \\
\end{align} $
Now, LCM will be $ 3\times 3\times 2\times 5=90 $
So, the total work will be 90 units.
Now, the efficiency of A will be $ \dfrac{90}{18}=5\text{ units} $
Now, the efficiency of B will be $ \dfrac{90}{15}=6\text{ units} $
We have given that B worked for 10 days and left the job. So the work done by B in 10 days will be $ 6\times 10=60\text{ units} $
Now, the work remaining will be $ 90-60=30\text{ units} $
So, the time taken by A to finish the remaining work will be $ =\dfrac{\text{work left}}{\text{efficiency}} $
 $ \Rightarrow \dfrac{30}{5}=6\text{ days} $
So, A alone can finish the remaining work in 6 days.

Note:
The possible mistake that a student can make in this question is considering that 10 days A and B work together which leads to incorrect solutions. The number of days to complete work decreases when the number of people increases. The key point to solving such types of questions is the calculation of the amount of work done by a person in a single day.