[2834] In an election between two candidates A and B, the number of valid votes received by A exceeds those

For Competitive Exams

In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?

2160

2420

2834

3150

Explanation:

Let the total number of votes polled in the election be 100k.

Number of valid votes = 100k - 20% (100k) = 80k

Let the number of votes polled in favour of A and B be a and b respectively.

a - b = 15% (100k) $\Rightarrow$ a = b + 15k

$\Rightarrow$ a + b = b + 15k + b

Now, 2b + 15k = 80k and hence b = 32.5k

It is given that 100k = 8720

32.5k = 32.5k/100k $\times$ 8720 = 2834

The number of valid votes polled in favour of B is 2834.

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