Question
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Answer: Option A
$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{ages}}\,{\text{of}}\,{\text{Kunal}}\,{\text{and}}\,{\text{Sagar}}\,{\text{6}}\,{\text{years}}\,{\text{ago}}\, \cr
& {\text{be}}\,6x\,{\text{and}}\,5x\,{\text{years}}\,{\text{respectively}} \cr
& {\text{Then,}}\,\frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr
& \Rightarrow 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr
& \Rightarrow 5x = 10 \cr
& \Rightarrow x = 2 \cr
& \therefore {\text{Sagar's}}\,{\text{present}}\,{\text{age}} \cr
& = \left( {5x + 6} \right)\,{\text{years}} \cr
& = 16\,{\text{years}}\, \cr} $$
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$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{ages}}\,{\text{of}}\,{\text{Kunal}}\,{\text{and}}\,{\text{Sagar}}\,{\text{6}}\,{\text{years}}\,{\text{ago}}\, \cr
& {\text{be}}\,6x\,{\text{and}}\,5x\,{\text{years}}\,{\text{respectively}} \cr
& {\text{Then,}}\,\frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr
& \Rightarrow 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr
& \Rightarrow 5x = 10 \cr
& \Rightarrow x = 2 \cr
& \therefore {\text{Sagar's}}\,{\text{present}}\,{\text{age}} \cr
& = \left( {5x + 6} \right)\,{\text{years}} \cr
& = 16\,{\text{years}}\, \cr} $$
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