I just wanted to know if there is any shortcut to solve this kind of questions orally,
The present ages of Shakti and Selene are in the ratio 10:3. After 3 years, the ratio becomes 23:9. Find the difference in their ages after 17 years.
(I know the approach in which you assume the common multiple to be x and solve the equation accordingly, just wanted to know if there's any shortcut, it would be great if anybody could help me, thanks! )
The $23:9$ is a giveaway. If Shakti is $23$ and Selene is $9$ at $3$ years from now, right now they are $20$ and $6$ respectively – which happens to be in the ratio $10:3$. So the difference in their ages is $14$, and this difference stays the same as they age, so the answer is $14$.