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?

A. 2160
B. 2420
C. 2834
D. 3150
E. None of these
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) => a = b + 15k
=> 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 * 8720 = 2834
The number of valid votes polled in favour of B is 2834.