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 ?

Answer: Option E

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)
$$\begin{array}{rl}& \therefore \frac{3x+2}{4x+2}=\frac{10}{13}\\ & \Rightarrow 13\left(3x+2\right)=10\left(4x+2\right)\\ & \Rightarrow 39x+26=40x+20\\ & \Rightarrow x=6\end{array}$$
Hence, Sarika's present age = 3x + 1
= (3 × 6 + 1) years
= 19 years