Question

Rahul and Karan finish off a task by themselves in $6$ and $8$ days respectively. If they worked on alternate days starting with Rahul for $5$ days and then Rahul goes away. In how many days will Karan finish the remaining task?

Answer 1

Find the number of days Karan takes to finish the remaining work:

Task completed by Rahul in one day $=\frac{1}{6}$

Task completed by Karan in one day $=\frac{1}{8}$

Task completed by Karan and Rahul in two days as they work on alternate days $=\frac{1}{6}+\frac{1}{8}=\frac{4+3}{24}=\frac{7}{24}$

If they worked on alternative days starting with Rahul for $5$days then work completed $=2\times \frac{7}{24}+\frac{1}{6}=\frac{9}{12}$

Let total work be $1$

The remaining work $=1-\frac{9}{12}=\frac{3}{12}$

Let the number of days required for Karan to complete the remaining task be $x$

Then, $\frac{1}{8}\times x=\frac{3}{12}$

$\Rightarrow x=\frac{3}{12}\times 8=2$

Hence, Karan needs $2$ days to complete the remaining task.