In an election, $15\%$ of voters did not cast their votes. Ratanbabu got $62.5\%$ of the votes cast and was declared elected by a majority of $3400$ votes. Find the total number of voters.

Let the total number of registered voters be $V$.
Since $15\%$ of voters did not vote, the total votes cast is:

$$\text{Votes Cast}=100\%-15\%=85\%\text{ of }V=0.85V$$

Ratanbabu received $62.5\%$ of the cast votes. The remaining votes went to his opponent:

$$\text{Opponent’s share}=100\%-62.5\%=37.5\%\text{ of the cast votes}$$

The margin of victory (majority) is the difference between Ratanbabu's votes and the opponent's votes:

$$\text{Margin}=62.5\%-37.5\%=25\%\text{ of the cast votes}$$

Given that the margin is $3400$ votes:

$$25\%\text{ of }(0.85V)=3400$$

$$\frac{1}{4}\times 0.85V=3400$$

$$0.85V=3400\times 4$$

$$0.85V=13600$$

$$V=\frac{13600}{0.85}=\frac{1360000}{85}=16000$$