Satyajit is younger than Diganta by $8$ years. If their ages are in the ratio of $5:7$, then how old is Satyajit?

Let the current ages of Satyajit and Diganta be $5k$ and $7k$ respectively.
According to the problem, Satyajit is $8$ years younger than Diganta:

$$7k-5k=8$$

$$2k=8$$

$$k=4$$

Now, determine the age of Satyajit:

$$\text{Age of Satyajit}=5k=5\times 4=20\text{ years}$$