In an election between R and S, R wins the election with $$\frac{1}{4}$$ votes of the votes polled in the favor of S. There are no invalid votes. What percentage(rounded off to 2 decimal places) of total votes are voted in favor of R?

Correct option is A

Given:

R wins election by a margin of $$\frac{1}{4}$$​ of total votes polled in favour of S

Solution:

Let the total votes polled be 100

And the total votes polled in favor of S =  x

Then total votes in favor of R = $$x + \frac{1}{4} of x = \frac{5x}{4}$$​​

Now total votes = $$x + \frac{5x}{4} =100$$​​

​$$\frac{4x +5x }{4} = 100$$​​

​$$x= \frac{400}{9}$$​​

Total votes in favor of R = $$\frac{5x}{4} = \frac{500}{9}$$​​

Percent of votes of R = $$\frac{\frac{500}{9}}{100} \times 100 = 55.56\%$$​​