Question

(Q.11) A mother is 3 times as old as her daughter.
5 years latter, the mother will be 2 and 1/2 times as old as her daughter.
Find the age of daughter and that of her mother in years.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{daughter}=\mathrm{x}\mathrm{yrs} \\ \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{mother}=\mathrm{y}\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{first}\mathrm{condition}: \\ \mathrm{y}=3\mathrm{x}....\left(1\right) \\ \mathrm{AFTER}5\mathrm{YEARS}: \\ \mathrm{daughter}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{x}+5\right)\mathrm{yrs} \\ \mathrm{mother}\text{'}\mathrm{s}\mathrm{age}=\left(\mathrm{y}+5\right)\mathrm{yrs} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{second}\mathrm{condition}: \\ \mathrm{y}+5=\frac{5}{2}\left(\mathrm{x}+5\right) \\ \Rightarrow 2\mathrm{y}+10=5\mathrm{x}+25 \\ \Rightarrow 2\mathrm{y}-5\mathrm{x}=15...\left(2\right) \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}\mathrm{from}\left(1\right)\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ 6\mathrm{x}-5\mathrm{x}=15 \\ \Rightarrow \mathrm{x}=15 \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{y}=3\times 15=45 \\ \mathrm{So},\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{daughter}=15\mathrm{yrs} \\ \mathrm{present}\mathrm{age}\mathrm{of}\mathrm{mother}=45\mathrm{yrs} \end{gathered}$$