Percent — Assertion Reason Type Questions

Assertion (A): 800 - 40% of 800 is 240.

Reason (R): 800 - 40% of 800 = 60% of 800.

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

40% of 800 $= \dfrac{40}{100} \times 800 = 320$.

∴ 800 − 40% of 800 = 800 − 320 = 480, and not 240.

Thus, Assertion (A) is false.

In percentage, the whole quantity is taken as 100%.

⇒ 800 - 40% of 800

⇒ (100 - 40)% of 800

⇒ 60% of 800

Thus, Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): 300 increases to 390. Increase% = 30%

Reason (R): Increase % = $\dfrac{\text{increase in value}}{\text{original value}}$ × 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 value = 300 and new value = 390.

Increase in value = 390 − 300 = 90.

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

⇒ Increase% = $\dfrac{9000}{300}$%

⇒ Increase% = 30%

Thus, Assertion (A) is true.

The formula to find the increase percent is

Increase% = $\dfrac{\text{Increase in value}}{\text{Original value}} \times 100$%, which is correct.

Thus, Reason (R) is true.

Hence, option 3 is the correct option.