Question

Arushi and Devesh are making a painting. Arushi can complete the painting in 30 minutes. Both Arushi and Devesh can complete the painting together in 20 minutes. They work (Painting)s together for 10 minutes and they have a quarrel. At this point, Arushi goes away. In how many minutes will Devesh finish the painting?

Answer 1

Hint: Given, the problem is based on time and work problems. In general if a person A completes a work in \[n\] days, then the work completed by him in one day is \[\left( {\dfrac{1}{n}} \right)\] . Conversely if a person p completes \[\left( {\dfrac{1}{n}} \right)\] work (Painting) in one day, then he will take \[n\] days to complete the work (Painting). We use this concept to solve this.

Complete step-by-step answer:
Given,
Arushi can complete the painting in 30 minute.
Therefore Arushi 1 minute work (Painting) \[ = \dfrac{1}{{30}}\]
If both Arushi and Devesh work (Painting) together they can complete the work (Painting) in 20 minute.
Therefore Arushi and Devesh 1 minute work (Painting) \[ = \dfrac{1}{{20}}\]
So we need the Devesh 1 minute work (Painting).
Devesh 1 minute work (Painting) = (Arushi and Devesh 1 minute work (Painting)) – (Arushi 1 minute work (Painting))
 \[ = \dfrac{1}{{20}} - \dfrac{1}{{30}}\]
 \[ = \dfrac{{3 - 2}}{{60}}\]
Devesh 1 minute work (Painting) \[ = \dfrac{1}{{60}}\] .
The amount of work (Painting) that can be done by Arushi and Devesh \[ = 10 \times \dfrac{1}{{30}}\]
 \[ = \dfrac{1}{3}\]
Reaming work (Painting) left after Arushi left \[ = 1 - \dfrac{1}{3}\]
 \[ = \dfrac{{3 - 1}}{3}\]
 \[ = \dfrac{2}{3}\] .
Devesh can complete \[\dfrac{1}{{60}}\] of the work (Painting) in one minute.
Therefore Devesh can complete 1 work (Painting) in 60 minute.
Hence, \[\dfrac{2}{3}\] of reaming work (Painting) will be completed by Devesh in,
 \[ = \dfrac{2}{3} \times 60\]
 \[ = 2 \times 20\]
 \[ = 40{\text{ minute}}\]
Hence, in 40 minute Devesh can complete the painting.
So, the correct answer is “40 minute”.

Note: Follow the same procedure for this kind of problem. We needed the work for painting done by Devesh after Arushi left, that's why we found the one minute work done by Devesh. It can be found by taking the difference of Arushi and Devesh 1 minute work and Arushi 1 minute work. We use the only used one concept that is in the hint part. Remember it will.