Question

A can paint a shed in 5 hours while B takes 6 hours to do the same job. A and B begin painting the shed together, but B is called away after sometime. A finished the remaining work in 1 hour 20 minutes. After how many hours did B leave?

Answer 1

Hint: So first find the work done in one hour by A and B separately. Let us assume B worked for x hours and left. So the total work done is equal to the work done by A and B in x hours plus the work done by A in 1 hour 20 minutes. Use this info to further solve the question.

Complete step by step solution:
We know that A takes 5 hours to finish the work; this means in one hour A can finish $ \dfrac{1}{5} $ th of the work and B takes 6 hours to finish the work; this means in one hour B can finish $ \dfrac{1}{6} $ th of the work.
A and B both work together; in one hour they can finish $ \left( {\dfrac{1}{5} + \dfrac{1}{6}} \right) $ th of the work.
Let us assume B left the work after x hours.
Total work done is equal to the sum of the work done by both A and B in x hours and the work done by A in 1 hour 20 minutes.
X is in hours so convert 1 hour 20 minutes into hours.
 $
  1hr = 60\min \\
   \Rightarrow 1\min = \dfrac{1}{{60}}hrs \\
   \Rightarrow {\text{1 hour 20 mins = 1}}hr + \dfrac{{20}}{{60}}hr \\
   \Rightarrow 1 + \dfrac{1}{3} = \dfrac{4}{3}hrs \\
  \therefore {\text{1 hour 20 mins}} = \dfrac{4}{3}hours \;
 $
Total work done is 1, which is equal to
 $
  x\left( {\dfrac{1}{5} + \dfrac{1}{6}} \right) + \dfrac{4}{3}\left( {\dfrac{1}{5}} \right) = 1 \\
   \Rightarrow x\left( {\dfrac{{11}}{{30}}} \right) + \dfrac{4}{{15}} = 1 \\
   \Rightarrow \dfrac{{11x}}{{30}} = 1 - \dfrac{4}{{15}} = \dfrac{{11}}{{15}} \\
   \Rightarrow \dfrac{x}{{30}} = \dfrac{1}{{15}} \\
   \Rightarrow x = \dfrac{{30}}{{15}} \\
  \therefore x = 2{\text{ hours}} \;
 $
Therefore, B left after $ 2\; hours $.

Note: As we can see the time taken by A to finish the remaining work is given in hours and minutes. But while solving a question, all the units must be the same which means either in hours or minutes. As the time when B left is asked in hours, the given time must be converted into hours. That is what we have done. And we have considered total work done as 1 because we divided the work done in fractions and when we sum up all those fractions, we get a result 1.