Question

If Sachin takes 10 days to complete work and Rohan takes 15 days to complete the same work. How many days will it take if both do the same work together?

Answer 1

Hint: First of all consider the total work as w. Now, find the work done by Sachin and Rohan in 1 day. Then add them and divide it by the total work to find the required answer.

Complete step-by-step solution:
In this question, we are given that Sachin takes 10 days to complete a work and Rohan takes 15 days to complete the same work. We have to find the number of days, the work will take if both do the same work together.
Let us consider the total work as w. We can say that the work done by Sachin in 10 days = w work. So, we get the work done by Sachin in 1 day as \[=\dfrac{w}{10}\text{work}\text{.}\]
Similarly, we can say that the work done by Rohan in 15 days = w work. So, we get the work done by Rohan in 1 day as \[=\dfrac{w}{15}\text{work}\text{.}\]
Therefore, we get the total work done by Sachin and Rohan in 1 day as
= Work done by Sachin in 1 day + work done by Rohan in 1 day
\[=\left( \dfrac{w}{10}+\dfrac{w}{15} \right)\text{work}\]
So, we get the work done by both Sachin and Rohan in 1 day as
\[=\dfrac{5w}{30}\text{work}\]
\[=\dfrac{w}{6}\text{work}\]
Let us consider that both of them together take t days to complete the work w. So, as we have found that in 1 day, they do \[\dfrac{w}{6}\text{work,}\] therefore in t days, they would do \[\left( \dfrac{w}{6}\times t \right)\text{work}\text{.}\] We know that the work done by them in t days = w work. So, we get,
\[\Rightarrow \dfrac{w}{6}\times t=w\]
\[\Rightarrow t=\dfrac{w}{\dfrac{w}{6}}\]
\[\Rightarrow t=\left( w\times \dfrac{6}{w} \right)\]
By cancelling the like term, we get,
\[\Rightarrow t=6\text{ }days\]
Hence, Sachin and Rohan will take 6 days to do the same work together.

Note: In these types of questions involving time and work, always find the work done by the person in 1 day or 1 hour, etc and then from that point, proceed further to find whatever is asked in the given question by using the unitary method. Also, always consider the total work as w, x, etc to clearly visualize the question. These methods will help in solving these types of questions very easily.