Percent and Percentage — Statement I-II Type Questions

Statement 1: x is 20% more than y, then y is 20% less than x.

Statement 2: % change = $\left(\dfrac{\text{Decrease (or increase) in the value}}{\text{Original value}} \times 100\right)$%

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Let y = 100.

x is 20% more than y

$\Rightarrow x = 100 + \dfrac{20}{100} \times 100$

= 100 + 20

= 120

Now, y is less than x by 120 − 100 = 20.

Percentage by which y is less than x

$= \left(\dfrac{20}{120} \times 100\right)$

$= \dfrac{2000}{120}$

$= \dfrac{50}{3}$

$= 16\dfrac{2}{3}$

Since y is $16\dfrac{2}{3}$% less than x and not 20% less than x, Statement 1 is false.

We know that,

% change = $\left(\dfrac{\text{Decrease (or increase) in the value}}{\text{Original value}} \times 100\right)$%

This is the correct formula. So, Statement 2 is true.

Statement 1 is false and Statement 2 is true.

Hence, option 4 is the correct option.

Statement 1: 2 min 24 seconds is 4% of 1 hour.

Statement 2: While comparing two quantities, they must be of the same kind and in the same units and required % = $\left(\dfrac{\text{Any Quantity}}{\text{Another Quantity}} \times 100\right)$%

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

We know, 1 hour = 60 × 60 seconds = 3600 seconds.

4% of 1 hour

$= \dfrac{4}{100} \times 3600 \text{ seconds}\\[1em] = \dfrac{14400}{100} \text{ seconds}\\[1em] = 144 \text{ seconds}$

Now, 144 seconds = (120 + 24) seconds = 2 min 24 seconds.

Since 4% of 1 hour = 2 min 24 seconds, Statement 1 is true.

We know that,

While comparing two quantities, they must be of the same kind and in the same units, and

required % = $\left(\dfrac{\text{Any Quantity}}{\text{Another Quantity}} \times 100\right)$%

This is correct. So, Statement 2 is true.

Both Statement 1 and Statement 2 are true.

Hence, option 1 is the correct option.