Question

From two numbers, subtract half of the smaller. The result for larger is 3× that of the smaller. What is their original ratio?

• A. 2 : 1
• B. 3 : 1
• C. 3 : 2
• D. None

Hint:

Introduce variables and write expressions exactly as described. Use algebra to find the ratio.

Answer 1

The Correct Option is A

Let the smaller number = \( x \), and the larger = \( y \), where \( y>x \).
We subtract half the smaller from both: - Smaller becomes: \( x - \frac{x}{2} = \frac{x}{2} \) - Larger becomes: \( y - \frac{x}{2} \) Given: \[ y - \frac{x}{2} = 3 \left( \frac{x}{2} \right) y - \frac{x}{2} = \frac{3x}{2} y = \frac{3x}{2} + \frac{x}{2} = \frac{4x}{2} = 2x \] \[ \boxed{y : x = 2 : 1} \]