Percent and Percentage — Assertion Reason Type Questions

Assertion (A): 7% of 12 km is 840 m.

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

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

7% of 12 km

$= \dfrac{7}{100} \times 12 \text{ km}\\[1em] = \dfrac{84}{100} \text{ km}\\[1em] = 0.84 \text{ km}$

We know, 1 km = 1000 m.

⇒ 0.84 km = 0.84 × 1000 m = 840 m

Since 7% of 12 km = 840 m, Assertion (A) is true.

We know that,

To find the percentage of a given quantity, we convert the percentage into a fraction and then 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 1 is the correct option.

Assertion (A): $2\dfrac{3}{4}$ as percent is 265%.

Reason (R): For converting a fraction or a decimal into a percentage, we multiply it by 100.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

$2\dfrac{3}{4} = \dfrac{11}{4}$

Converting $\dfrac{11}{4}$ into percent,

$= \left(\dfrac{11}{4} \times 100\right)$

Since $2\dfrac{3}{4}$ as percent is 275% and not 265%, Assertion (A) is false.

We know that,

For converting a fraction or a decimal into a percentage, we multiply it by 100 and put the % sign. So, Reason (R) is true.

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

Hence, option 2 is the correct option.

Assertion (A): Daily attendance is reduced to 210 from 300, the decrease % is 30%.

Reason (R): % decrease = $\dfrac{\text{Decrease}}{\text{Original value}} \times 100$%

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Original attendance = 300 and reduced attendance = 210.

Decrease in attendance = 300 − 210 = 90

Percentage decrease:

$= \left(\dfrac{\text{Decrease}}{\text{Original value}} \times 100\right)$

$= \left(\dfrac{90}{300} \times 100\right)$

$= \dfrac{9000}{300}$

$= 30$

Since the decrease percent is 30%, Assertion (A) is true.

We know that,

% decrease = $\left(\dfrac{\text{Decrease}}{\text{Original value}} \times 100\right)$%. So, Reason (R) is true.

Both Assertion (A) and Reason (R) are true.

Hence, option 3 is the correct option.