Question

Jagdish can build a wall in $10$ days. Narender can build the same wall in $12$ days while Sumit takes $15$ days to do the same job. Which two of them should be employed to finish the job in $6$ days?

Answer 1

Find the time taken by employees to complete the task when working together :

Given, Jagdish builds a wall in $10$ days, Narender can build the same wall in $12$ days and Sumit takes $15$ days to build the same wall.

Here, we have to find out which of the two will do this same work together within $6$ days.

So, if we find the efficiency of all the workers, then we can find the work they can do in one day. And this work done in one day is known as efficiency for that.

The work done by Jagdish in one day $=\frac{1}{10}$

The work done by Narender in one day $=\frac{1}{12}$

The work done by Sumit in one day $=\frac{1}{15}$

If Jagdish and Sumit work together, then work done by both Jagdish and Sumit in one day is,

$$\begin{gathered} =\frac{1}{10}+\frac{1}{15} \\ =\frac{15+10}{150} \\ =\frac{25}{150} \\ =\frac{1}{6} \end{gathered}$$

So, the total number of days required for Jagdish and Sumit to complete the work $=6$ days.

Hence, Jagdish and Sumit should be employed together to finish the job in $6$ days.