#### Question

Aasheesh can paint his doll in 20 minutes and his sister Chinki can do so in 25 minutes. They paint the doll together for five minutes. At this juncture they have a quarrel and Chinki withdraws from painting. In how many minutes will Aasheesh finish the painting of the remaining doll?

#### Solution

\[\text{ Aasheesh can paint a doll in 20 minutes, and Chinki can do the same in 25 minutes } . \]

\[ \therefore \text{ Work done by Aasheesh in 1 minute } = \frac{1}{20}\]

\[ \therefore \text{ Work done by Chinki in 1 minute } = \frac{1}{25}\]

\[ \therefore \text{ Work done by them together } = \frac{1}{20} + \frac{1}{25}\]

\[ = \frac{5 + 4}{100} = \frac{9}{100}\]

\[ \therefore \text{ Work done by them in 5 minutes } = 5 \times \frac{9}{100} = \frac{9}{20}\]

\[\text{ Remaining work } = 1 - \frac{9}{20} = \frac{11}{20}\]

\[\text{ It is given that the remaining work is done by Aasheesh } . \]

\[ \text{ The work done by Aasheesh in 20 minutes . } \]

\[ \therefore \frac{11}{20}th \text{ work will be done by Aasheesh in } \left( 20 \times \frac{11}{20} \right) \text{ minutes or 11 minutes } . \]

\[\text{ Thus, the remaining work is done by Aasheesh in 11 minutes } .\]

\[ \therefore \text{ Work done by Aasheesh in 1 minute } = \frac{1}{20}\]

\[ \therefore \text{ Work done by Chinki in 1 minute } = \frac{1}{25}\]

\[ \therefore \text{ Work done by them together } = \frac{1}{20} + \frac{1}{25}\]

\[ = \frac{5 + 4}{100} = \frac{9}{100}\]

\[ \therefore \text{ Work done by them in 5 minutes } = 5 \times \frac{9}{100} = \frac{9}{20}\]

\[\text{ Remaining work } = 1 - \frac{9}{20} = \frac{11}{20}\]

\[\text{ It is given that the remaining work is done by Aasheesh } . \]

\[ \text{ The work done by Aasheesh in 20 minutes . } \]

\[ \therefore \frac{11}{20}th \text{ work will be done by Aasheesh in } \left( 20 \times \frac{11}{20} \right) \text{ minutes or 11 minutes } . \]

\[\text{ Thus, the remaining work is done by Aasheesh in 11 minutes } .\]

Is there an error in this question or solution?

Solution Aasheesh Can Paint His Doll in 20 Minutes and His Sister Chinki Can Do So in 25 Minutes. They Paint the Doll Together for Five Minutes. Concept: Time and Work.