Directions:

In a scholarship screening, 50% of the applicants qualified in Economics and 37.5% qualified in Sociology. No applicant failed in both subjects. If 75 applicants did not qualify in Sociology, how many applicants did not qualify in Economics?

The correct answer is 60.

Step 1: Understand the given data
Let the total number of scholarship applicants be represented as 100%.
Percentage of applicants who qualified in Economics = 50%
Percentage of applicants who qualified in Sociology = 37.5%
Number of applicants who did not qualify in Sociology = 75

Step 2: Calculate the total number of applicants
The percentage of applicants who did not qualify in Sociology is:

$100\%-37.5\%=62.5\%$

We are given that 62.5% of the total number of applicants equals 75 applicants.
Let $T$ be the total number of applicants:

$62.5\%\text{of}T=75$

$0.625\times T=75$

$T=\frac{75}{0.625}=120$

Thus, the total number of applicants is 120.

Step 3: Calculate the number of applicants who did not qualify in Economics
The percentage of applicants who did not qualify in Economics is:

$100\%-50\%=50\%$

Now, calculate 50% of the total 120 applicants:

$\text{Applicants not qualifying in Economics}=50\%\text{of}120$

$\text{Applicants not qualifying in Economics}=0.50\times 120=60$

Therefore, 60 applicants did not qualify in Economics.