In an election two candidates participated, the winner got 60% of the total valid votes, 30% of the votes were declared as invalid. If the total number of votes was 8000, the number of valid votes that the other candidate got was.

The correct answer is 2240.

Let's step through the solution step-by-step to find the number of valid votes obtained by the losing candidate.

Step 1: Calculate the total number of valid votes
We are given that the total number of votes cast is 8000.
Since 30% of the total votes were declared invalid, the percentage of valid votes is:
100% - 30% = 70%

Now, let's calculate the exact number of valid votes:

$\text{Total Valid Votes}=70\%\text{ of }8000$

$\text{Total Valid Votes}=\frac{70}{100}\times 8000=5600$

Step 2: Calculate the percentage of valid votes the other candidate received
The winning candidate received 60% of the total valid votes.
Therefore, the other (losing) candidate must have received the remaining valid votes:
100% - 60% = 40%

Step 3: Calculate the number of valid votes for the other candidate
Now we calculate 40% of the total valid votes (5600):

$\text{Votes of Other Candidate}=40\%\text{ of }5600$

$\text{Votes of Other Candidate}=\frac{40}{100}\times 5600$

$\text{Votes of Other Candidate}=40\times 56=2240$

Thus, the number of valid votes obtained by the other candidate is 2240.