Ratio & Proportion — Assertion-Reason Questions

Assertion (A): The ratio of 30 minutes to 2 hours is 1 : 4.

Reason (R): Ratio exists between two quantities of the same kind and in the same units.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

Convert 2 hours into minutes: 2 hours = 2 × 60 = 120 minutes.

Ratio of 30 minutes to 2 hours = 30 : 120 = $\dfrac{30}{120} = \dfrac{1}{4}$ = 1 : 4.

So, Assertion (A) is true.

Ratio exists between two quantities of the same kind and in the same units. This is a correct statement, and it is exactly why the two times were first converted into the same unit (minutes) before finding the ratio.

So, Reason (R) is true and it correctly explains the Assertion (A).

Hence, option 1 is the correct option.

Assertion (A): The numbers a, b, c, d are said to be in proportion, if and only if ad = bc.

Reason (R): The order of terms in a proportion does not matter.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

The numbers a, b, c, d are in proportion if and only if the product of extremes equals the product of means, i.e. ad = bc.

So, Assertion (A) is true.

The order of terms in a proportion does matter. For example, 2 : 3 :: 4 : 6 is a proportion, but changing the order to 3 : 2 :: 4 : 6 is not. So the Reason (R) is a false statement.

So, Reason (R) is false.

Hence, option 3 is the correct option.