Percentage — Assertion-Reason Questions

Assertion (A): When an improper fraction is converted into a percentage, then the answer is always greater than 100.

Reason (R): In any question, % sign can be replaced with $\dfrac{1}{100}$.

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

An improper fraction is always greater than 1. On multiplying it by 100, the result is always greater than 100.

For example, $\dfrac{5}{4} = \left(\dfrac{5}{4} \times 100\right)$% = 125% > 100%.

So, Assertion (A) is true.

We know that % means per hundred, so in any question the % sign can be replaced with $\dfrac{1}{100}$. So, Reason (R) is true.

However, the Assertion follows from the fact that a fraction or decimal is converted into a percentage by multiplying it by 100, and not from replacing the % sign with $\dfrac{1}{100}$. So, Reason (R) is not the correct explanation of Assertion (A).

Hence, option 2 is the correct option.

Assertion (A): Out of 600 students of a school, 150 go for a picnic. The percentage of students that did not go for the picnic is 75.

Reason (R): To find the percentage of a given quantity, convert the given percentage into a fraction and divide by the given quantity.

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

Total number of students = 600.

Number of students who went for the picnic = 150.

Number of students who did not go for the picnic = 600 − 150 = 450.

Percentage of students who did not go for the picnic = $\left(\dfrac{450}{600} \times 100\right)$%

$= \dfrac{45000}{600}$%

= 75%

So, Assertion (A) is true.

To find the percentage of a given quantity, we convert the given percentage into a fraction and multiply it by the given quantity, and not divide it by the given quantity. So, Reason (R) is false.

Assertion (A) is true and Reason (R) is false.

Hence, option 3 is the correct option.