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?

Answer 1

$$\begin{gathered} \mathrm{Aasheesh}\mathrm{can}\mathrm{paint}\mathrm{a}\mathrm{doll}\mathrm{in}20\mathrm{minutes},\mathrm{and}\mathrm{Chinki}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{same}\mathrm{in}25\mathrm{minutes}. \\ \therefore \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Aasheesh}\mathrm{in}1\mathrm{minute}=\frac{1}{20} \\ \therefore \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Chinki}\mathrm{in}1\mathrm{minute}=\frac{1}{25} \\ \therefore \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{them}\mathrm{together}=\frac{1}{20}+\frac{1}{25} \\ =\frac{5+4}{100}=\frac{9}{100} \\ \therefore \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{them}\mathrm{in}5\mathrm{minutes}=5\times \frac{9}{100}=\frac{9}{20} \\ \mathrm{Remaining}\mathrm{work}=1-\frac{9}{20}=\frac{11}{20} \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{remaining}\mathrm{work}\mathrm{is}\mathrm{done}\mathrm{by}\mathrm{Aasheesh}. \\ \text{The}\mathrm{work}\mathrm{done}\mathrm{by}\mathrm{Aasheesh}\mathrm{in}20\mathrm{minutes}. \\ \therefore \frac{11}{20}\text{th}\mathrm{work}\mathrm{will}\mathrm{be}\mathrm{done}\mathrm{by}\mathrm{Aasheesh}\mathrm{in}\left(20\times \frac{11}{20}\right)\mathrm{minutes}\mathrm{or}11\mathrm{minutes}. \\ \mathrm{Thus},\mathrm{the}\mathrm{remaining}\mathrm{work}\mathrm{is}\mathrm{done}\mathrm{by}\mathrm{Aasheesh}\mathrm{in}11\mathrm{minutes}. \end{gathered}$$