raj and bala participated in a college election. raj collected 71% votes and won with a margin of 840 votes.how many were the total votes

Let x be the number of total votes. Then Raj collected 0.71x and Bala collected 0.29x.

$${\mathtt{0.71}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{0.29}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{840}} \Rightarrow {\mathtt{x}} = {\mathtt{2\,000}}$$

So there are 2000 votes in total.