Question

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?

Answer 1

The number of valid votes B got is 2834.

Explanation

Total number of votes polled = 8720

Number of invalid votes = 20% of 8720 = $(0.20*8720)=1744$

So, the number of valid votes = 8720-1744 = 6976

Now, 15% of the total number of votes polled $=(0.15*8720)=1308$

That means, the number of valid votes received by A exceeds those received by B by 1308.

Suppose, the number of valid votes received by B is $x$

So, the number of valid votes received by A will be : $(x+1308)$

As the total number of valid votes is 6976, so....

$x+(x+1308)=6976\\ \\ 2x+1308=6976\\ \\ 2x=6976-1308=5668\\ \\ x= \frac{5668}{2}=2834$

Thus, the the number of valid votes B got is 2834.