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: Let B = x.
Given that A exceeds B by 50%, we have: \[ A = x + 50% \times x = 1.5x \]

Step 2: B is less than C by 25%, so:
\[ B = C - 25% \times C = 0.75C \] Thus, \( C = \frac{B}{0.75} = \frac{x}{0.75} = \frac{4x}{3} \).

Step 3: Ratio of A to C.
We have \( A = 1.5x \) and \( C = \frac{4x}{3} \). Therefore, the ratio \( A : C \) is: \[ A : C = \frac{1.5x}{\frac{4x}{3}} = \frac{1.5 \times 3}{4} = \frac{4.5}{4} = \frac{9}{8} \] Thus, the correct ratio is \( A : C = 9 : 8 \).

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