Question

If 100 fewer students had applied and 50 fewer were selected, the ratio selected:unselected would be \(7:4\). In reality, the ratio selected:unselected was \(3:2\). How many students had applied?

• A. 325
• B. 415
• C. 375
• D. 425

Hint:

Translate ratio statements into variables first (\(3k,2k\)). For “if less/more” scenarios, adjust both selected and unselected consistently before forming the new ratio.

Answer 1

The Correct Option is C

Step 1: Initial Ratio
Assume selected and unselected applicants are in the ratio \(3:2\).
Let selected \(=3k\), unselected \(=2k\), and total applicants \(A=5k\).
Step 2: Apply the Change
If \(100\) applicants are removed: applied \(A-100\), selected \(3k-50\). Unselected becomes \((A-100)-(3k-50)=(2k-50)\).
The new ratio of selected to unselected is \((3k-50):(2k-50)=7:4\).
Step 3: Solve for \(k\)
Solve for \(k\): \(\displaystyle \frac{3k-50}{2k-50}=\frac{7}{4}\Rightarrow 4(3k-50)=7(2k-50)\Rightarrow 12k-200=14k-350\Rightarrow 2k=150\Rightarrow k=75.\)
Calculate the total number of applicants: \(A=5k=375\).
\[ \boxed{375} \]