In an election between two candidates, one got 60% of the total valid votes and 15% of the votes were invalid. If the total number of votes were 8400, the number of valid votes that the other candidate got were:

The correct answer is 2856.

Step-by-step explanation:

1. Find the total number of valid votes:
The total number of votes cast is 8400.
It is given that 15% of the total votes were invalid.
Therefore, the percentage of valid votes is:
$100\%-15\%=85\%$

Now, calculate the total number of valid votes:
$\text{Total Valid Votes}=85\%\text{of}8400$

$\text{Total Valid Votes}=\frac{85}{100}\times 8400=85\times 84=7140$

2. Find the percentage of valid votes received by the second candidate:
The first candidate received 60% of the total valid votes.
Since the total valid votes represent 100%, the percentage of valid votes received by the other candidate is:
$100\%-60\%=40\%$

3. Calculate the number of valid votes received by the other candidate:
$\text{Valid votes for the other candidate}=40\%\text{of}7140$

$\text{Valid votes for the other candidate}=\frac{40}{100}\times 7140=4\times 714=2856$

Thus, the number of valid votes that the other candidate got is 2856.