Question

If A:B = 8:15, B:C = 5:8 and C:D = 4:5, then A:D is equal to:

• A. 2:7
• B. 4:15
• C. 8:15
• D. 15:4

Hint:

To find A:D from a chain of ratios, multiply all the intermediate ratios and simplify step by step. Cancel common terms early to make calculations easier.

Answer 1

The Correct Option is B

We are given: \[ \text{A:B} = 8:15,\quad \text{B:C} = 5:8,\quad \text{C:D} = 4:5 \] To find A:D, we multiply all three ratios together: \[ \frac{A}{D} = \frac{A}{B} \times \frac{B}{C} \times \frac{C}{D} \] \[ \frac{A}{D} = \frac{8}{15} \times \frac{5}{8} \times \frac{4}{5} \] Now simplify step by step using the aligned environment: \[ \begin{aligned} \frac{A}{D} &= \left( \frac{8}{15} \times \frac{5}{8} \right) \times \frac{4}{5} \\ &= \left( \frac{1}{3} \right) \times \frac{4}{5} \\ &= \frac{4}{15} \end{aligned} \] Thus, A:D = 4:15