Question

Anmol'sage is six times his son's age .Four years hence,the age of anmol will be four times his sons age.The present age in years,of the father and the son are res.?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{Anmol}\text{'}\mathrm{s}\mathrm{age}=x\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{son}\text{'}\mathrm{s}\mathrm{age}=y\mathrm{yrs} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{first}\mathrm{condition}, \\ x=6y.......\left(1\right) \\ \underline{\mathrm{After}4\mathrm{years}:} \\ \mathrm{Anmol}\text{'}\mathrm{s}\mathrm{age}=\left(x+4\right)\mathrm{yrs} \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=\left(y+4\right)\mathrm{yrs} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{second}\mathrm{condition}, \\ x+4=4\left(y+4\right) \\ \Rightarrow x+4=4y+16 \\ \Rightarrow x-4y=12.......\left(2\right) \\ \mathrm{putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{from}\left(1\right)\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ 6y-4y=12 \\ \Rightarrow 2y=12 \\ \Rightarrow y=6 \\ \mathrm{now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ x=6\times 6=36 \\ \mathrm{so},\mathrm{Anmol}\text{'}\mathrm{s}\mathrm{age}=36\mathrm{yrs} \\ \mathrm{son}\text{'}\mathrm{s}\mathrm{age}=6\mathrm{yrs} \end{gathered}$$