In an election between two candidates, one got 60% of the total valid votes. 25% of the votes were invalid. If the total number of votes was 15,000, then find the number of valid votes that the other candidate got.

The correct answer is 4,500.

Step 1: Understand the given information
We are given the following parameters from the problem:
Total number of votes = 15,000
Percentage of invalid votes = 25%
Percentage of valid votes secured by one candidate = 60%

Step 2: Calculate the total number of valid votes
Since 25% of the total votes were invalid, the valid votes constitute the remaining 75% of the total votes.

$\text{Percentage of valid votes}=100\%-25\%=75\%$

Now, calculate 75% of the 15,000 total votes:

$\text{Total valid votes}=\frac{75}{100}\times \mathrm{15,000}$

$\text{Total valid votes}=0.75\times \mathrm{15,000}=\mathrm{11,250}$

Step 3: Find the percentage of valid votes received by the other candidate
The total valid votes represent 100% of the valid vote count. If one candidate got 60% of these valid votes, then the other candidate must have received:

$\text{Percentage for the other candidate}=100\%-60\%=40\%$

Step 4: Calculate the number of valid votes the other candidate received
Finally, calculate 40% of the total valid votes (11,250):

$\text{Valid votes for the other candidate}=\frac{40}{100}\times \mathrm{11,250}$

$\text{Valid votes for the other candidate}=0.40\times \mathrm{11,250}=\mathrm{4,500}$

Thus, the number of valid votes that the other candidate got is 4,500.