Question

A:B = 4:5, B:C = 6:7, what is the value of A:C?

• A. 24:35
• B. 24:36
• C. 28:35
• D. 30:35

Hint:

When solving ratio problems, make sure to express all quantities in terms of a common variable to simplify comparisons.

Answer 1

The Correct Option is A

We are given the ratios A:B = 4:5 and B:C = 6:7. To find A:C, we first need to eliminate B. - From A:B = 4:5, we can write A = 4x and B = 5x. - From B:C = 6:7, we can write B = 6y and C = 7y. Now, equate the two expressions for B: \[ 5x = 6y \quad \Rightarrow \quad x = \frac{6y}{5} \] Substitute x into A = 4x: \[ A = 4 \times \frac{6y}{5} = \frac{24y}{5} \] Now, A:C = \frac{24y}{5} : 7y = 24:35.