Question

Assertion (A): If $$\frac{a}{b} = \frac{c}{d}$$, then $$\frac{a + c}{b + d} = \frac{a}{b}$$.

Reason (R): If two or more than two ratios are equal, then, each ratio = $$\frac{\text{sum of antecedents}}{\text{sum of consequents}}$$

पर्याय

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct explanation of A.

Explanation:

Step 1 – Assertion: A is true. Since the ratios are equal, their combined ratio equals either ratio: $$\frac{a+c}{b+d}=\frac{a}{b}=\frac{c}{d}.$$

Step 2 – Reason: R is true. The provided property states that if two or more ratios are equal, each ratio equals the sum of antecedents divided by the sum of consequents.

Step 3 – Link: Applying this property to the two equal ratios gives $$\frac{a+c}{b+d}=\frac{a}{b}$$, so R correctly explains A.