Question

If A exceeds B by 50% and B is less than C by 25%, then A : C is:

• A. 2:1
• B. 1:8
• C. 3:8
• D. 9:8

Hint:

When dealing with percentage increase or decrease, convert the percentages to fractions and express the relationship algebraically.

Answer 1

The Correct Option is A

Step 1: Define B.
Let B equal x. Since A exceeds B by 50%, the equation for A is: \[ A = x + 0.50x = 1.5x \]

Step 2: Relate B and C.
B is 25% less than C, which can be expressed as: \[ B = C - 0.25C = 0.75C \] This implies that \( C = \frac{B}{0.75} = \frac{x}{0.75} = \frac{4x}{3} \).

Step 3: Calculate the ratio A to C.
Using the derived values \( A = 1.5x \) and \( C = \frac{4x}{3} \), the ratio \( A : C \) is computed as: \[ A : C = \frac{1.5x}{\frac{4x}{3}} = \frac{1.5 \times 3}{4} = \frac{4.5}{4} = \frac{9}{8} \] Therefore, the ratio \( A : C \) is \( 9 : 8 \).

Final Answer: \[ \boxed{9:8} \]