One year ago the ratio of the ages of Sarika and Gouri was 3 : 4 respectively. One year hence the ratio of their ages will be 10 : 13 respectively. What is Sarika's present age ?

Solution (By Examveda Team)

Let Sarika's and Gauri's ages one year ago be 3x and 4x years respectively
Sarika's age 1 year hence = (3x + 2) years
Gauri's age 1 year hence = (4x + 2)
$$\eqalign{ & \therefore \frac{{3x + 2}}{{4x + 2}} = \frac{{10}}{{13}} \cr & \Rightarrow 13\left( {3x + 2} \right) = 10\left( {4x + 2} \right) \cr & \Rightarrow 39x + 26 = 40x + 20 \cr & \Rightarrow x = 6 \cr} $$
Hence, Sarika's present age = 3x + 1
= (3 × 6 + 1) years
= 19 years