Question

From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?

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

Hint:

Call the smaller number b and the larger a, and write the two new numbers.

Answer 1

The Correct Option is A

Step 1: Set up:
Let the numbers be \(a\) (larger) and \(b\) (smaller). After subtracting \(\dfrac b2\), they become \(a - \dfrac b2\) and \(\dfrac b2\).

Step 2: Use the condition:
The larger new number is \(a - \dfrac b2\) and it equals \(3 \times \dfrac b2\). So \(a = \dfrac{3b}{2} + \dfrac b2 = 2b\).

Step 3: Ratio:
\(a : b = 2 : 1\). Check with \(b = 2, a = 4\): the new numbers are 3 and 1, and \(3 = 3 \times 1\).

Final Answer:
The correct option is (1): 2 : 1.