Percent — Statement I-II Type Questions

Statement 1: Out of 1000 students 60% are boys and the rest are girls. The number of girls is 600.

Statement 2: The number of boys is 600.

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

Total number of students = 1000 and percentage of boys = 60%.

Number of boys = 60% of 1000

= $\dfrac{60}{100} \times 1000$

= $\dfrac{60000}{100}$

= 600

Number of girls = 1000 − 600 = 400.

The number of girls is 400 and not 600.

Thus, statement 1 is false.

The number of boys is 600, as calculated above.

Thus, statement 2 is true.

Hence, option 4 is the correct option.

Statement 1: 10% of 600 + 15% of 600 = 150.

Statement 2: 10% of 600 + 15% of 600 = 25% of 600 = $\dfrac{25}{100}$ × 600 = 150

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

Solving,

⇒ 10% of 600 + 15% of 600

$\Rightarrow \dfrac{10}{100} \times 600 + \dfrac{15}{100} \times 600$

⇒ 60 + 90

⇒ 150

So, 10% of 600 + 15% of 600 = 150.

Thus, statement 1 is true.

Since both the percentages are taken of the same quantity 600, they can be added.

⇒ (10% + 15%) of 600

⇒ 25% of 600

$\Rightarrow \dfrac{25}{100} \times 600$

⇒ 150

Thus, statement 2 is true.

Hence, option 1 is the correct option.