Question

A can finish a piece of work in 15 days and B can do it in 10 days. They worked together for 2 days and then B went away. In how many days will A finish the remaining work?
A. 14 days
B. 17 days
C. 12 days
D. 10 days

Answer 1

Hint: We will first find out the work done by A and B in 1 day. Then we will find the total work done by A and B together in 1 day. As it is given that they worked together for 2 days, we will find the work completed by them in two days. Then we will find the remaining fraction of work by subtracting it from 1.

Complete step by step solution:
In the question we are given that A can finish a piece of work in 15 days and B can do it in 10 days. It is given that they worked together for 2 days and then B goes away and we are asked to find the number of days in which A will finish the remaining work.
So, in the question it is given that A can finish the whole work in 15 days, so we can conclude that,
In 1 day A can complete $\dfrac{1}{15}$ of the work.
It is also given that B can finish the whole work in 10 days. So, from this we can conclude that,
In 1 day B can complete $\dfrac{1}{10}$ of the work.
So, if both A and B work together, then we can say that,
In 1 day A and B together can complete $\left( \dfrac{1}{15}+\dfrac{1}{10} \right)$ of the work.
So, we will first simplify this by taking the LCM and get,
$\left( \dfrac{1}{15}+\dfrac{1}{10} \right)=\left( \dfrac{2+3}{30} \right)=\dfrac{5}{30}=\dfrac{1}{6}$
Thus, we can say that A and B together can complete $\dfrac{1}{6}$ of the work in 1 day.
Now, it is given that they worked together for 2 days. So, the work they complete together in 2 days will be, $2\times \dfrac{1}{6}=\dfrac{1}{3}$. Hence, after 2 days the work completed is $\dfrac{1}{3}$. So, the total work left to be completed is given as, $1-\dfrac{1}{3}=\dfrac{2}{3}$. So, we can say that $\dfrac{2}{3}$ amount of work has to be done by A.
We know that A can complete $\dfrac{1}{15}$ of the work in 1 day. So, A can complete the whole work in 15 days.
So, A can complete $\dfrac{2}{3}$ of the work left to be completed in $\left( \dfrac{2}{3}\times 15 \right)=10$ days.
Therefore, the correct option is option D.

Note: The possible mistakes that the students can make in this question is by considering the total number of days, that is (15+10) = 25 as the total amount of work, so they will write the remaining amount of work to be done by A as $25-\dfrac{1}{3}$ and will end up getting the wrong answers. Another mistake is that in the end, after finding the final answer, that is 10 days, they may add another 2 days, that is when A and B both worked together, with it and will get the answer as 12 days and will write option (C) as the answer but this is not correct.