Question

Ali's and Karan's present ages are in the ratio of 7:10. Find their present ages if five years from now the ratio of their ages will be 8:11.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Ali}\mathrm{and}\mathrm{karan}\mathrm{be}7\mathrm{x}\mathrm{and}10\mathrm{x} \\ \mathrm{After}5\mathrm{years},\mathrm{their}\mathrm{ages}\mathrm{will}\mathrm{be}7\mathrm{x}+5\mathrm{and}10\mathrm{x}+5 \\ \frac{7\mathrm{x}+5}{10\mathrm{x}+5}=\frac{8}{11} \\ \Rightarrow 11\left(7\mathrm{x}+5\right)=8\left(10\mathrm{x}+5\right) \\ \Rightarrow 77\mathrm{x}+55=80\mathrm{x}+40 \\ \Rightarrow 55-40=80\mathrm{x}-77\mathrm{x} \\ \Rightarrow 15=3\mathrm{x} \\ \Rightarrow \mathrm{x}=5 \\ \mathrm{So}\mathrm{present}\mathrm{ages}\mathrm{of}\mathrm{ali}\mathrm{and}\mathrm{karan}\mathrm{are}: \\ 7\mathrm{x}=7\times 5=35\mathrm{yrs} \\ 10\mathrm{x}=10\times 5=50\mathrm{yrs} \end{gathered}$$
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