KnowledgeBoat Logo
|

Mathematics

a, b, c and d are in proportion.

Assertion (A): a + b, a - b, c + d and c - d are in proportion.

Reason (R): ab=cd\dfrac{a}{b} = \dfrac{c}{d}.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Ratio Proportion

1 Like

Answer

Given,

a, b, c and d are in proportion.

∴ab=cd\therefore \dfrac{a}{b} = \dfrac{c}{d}

So, reason (R) is true.

Applying componendo and dividendo, we get

⇒a+ba−b=c+dc−d\Rightarrow \dfrac{a + b}{a - b} = \dfrac{c + d}{c - d}

Therefore, a + b, a - b, c + d and c - d are in proportion.

So, assertion (A) is true and reason (R) correctly explains assertion (A).

Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

Answered By

3 Likes

Related Questions