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?

116 years
218 years
320 years
4Cannot be determined

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let the ages of Kunal and Sagar 6 years ago \\ be 6 x and 5 x years respectively \\ Then, \frac{(6 x + 6) + 4}{(5 x + 6) + 4} = \frac{11}{10} \\ \Rightarrow 10 (6 x + 10) = 11 (5 x + 10) \\ \Rightarrow 5 x = 10 \\ \Rightarrow x = 2 \\ ∴ Sagar's present age \\ = (5 x + 6) years \\ = 16 years \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{ages}}\,{\text{of}}\,{\text{Kunal}}\,{\text{and}}\,{\text{Sagar}}\,{\text{6}}\,{\text{years}}\,{\text{ago}}\, \cr & {\text{be}}\,6x\,{\text{and}}\,5x\,{\text{years}}\,{\text{respectively}} \cr & {\text{Then,}}\,\frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr & \Rightarrow 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr & \Rightarrow 5x = 10 \cr & \Rightarrow x = 2 \cr & \therefore {\text{Sagar's}}\,{\text{present}}\,{\text{age}} \cr & = \left( {5x + 6} \right)\,{\text{years}} \cr & = 16\,{\text{years}}\, \cr}$