Question

If A : B = 2 : 3 and B : C = 4 : 5, find the ratio A : C.

• A. 2 : 5
• B. 8 : 15
• C. 3 : 5
• D. 8 : 12
• E. 6 : 15

Hint:

For finding the ratio of the first term to the last term in a chain of ratios, multiplying all the given fractions is the fastest and most direct method.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given two separate ratios that share a common element (\(B\)). We need to combine these to find the direct ratio between the first element (\(A\)) and the last element (\(C\)).


Step 2: Key Formula or Approach:
To find a compound ratio \(\frac{A}{C}\) from \(\frac{A}{B}\) and \(\frac{B}{C}\), simply multiply the two given fractions together. The common variable \(B\) will cancel out.


Step 3: Detailed Explanation:
Given ratios: \[ \frac{A}{B} = \frac{2}{3} \] \[ \frac{B}{C} = \frac{4}{5} \] Multiply the two ratios to find \(\frac{A}{C}\): \[ \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \] Substitute the given values: \[ \frac{A}{C} = \frac{2}{3} \times \frac{4}{5} \] \[ \frac{A}{C} = \frac{2 \times 4}{3 \times 5} \] \[ \frac{A}{C} = \frac{8}{15} \] This gives the ratio A : C = 8 : 15.


Step 4: Final Answer:
The ratio A : C is 8 : 15.