## To find the number of votes secured by each candidate, we'll work backwards by setting up an equation based on the given information.

Let's assume the total number of votes is represented by 2x, where x is a variable.

According to the given information, if the rival candidate obtained 1/6th of the total votes secured by the successful candidate in addition to his own votes, he would have won the elections by 42 votes.

So, we can set up the equation:

x + 42 = (x/6) + (2x - 236)

Let's simplify the equation step by step:

First, let's simplify the right side of the equation:

(x/6) + (2x - 236)

= x/6 + 2x - 236

= (x + 12x - 1416)/6

= (13x - 1416)/6

Now, we can substitute this simplified expression back into the equation:

x + 42 = (13x - 1416)/6

To get rid of the fraction, we can multiply both sides of the equation by the denominator (6):

6(x + 42) = 13x - 1416

Now, distribute the 6 on the left side:

6x + 252 = 13x - 1416

Next, let's isolate the x term by moving the constant terms to the right side:

13x - 6x = 1416 + 252

7x = 1668

To solve for x, divide both sides of the equation by 7:

x = 1668/7

x = 238

So, the total number of votes is 2x, which is 2 * 238 = 476.

Now, we can find the number of votes secured by each candidate:

Successful candidate: 2x - 236 = 2 * 238 - 236 = 240 votes

Rival candidate: x = 238 votes

Therefore, the successful candidate secured 240 votes and the rival candidate secured 238 votes.