Percent and Percentage — Multiple Choice Questions

In the ratio 1 : 2 : 5, the middle term as percentage of the whole is:

1. 20%

2. 10%

3. 25%

4. 31.5%

Answer

Ratio = 1 : 2 : 5, so the whole = 1 + 2 + 5 = 8 and the middle term = 2.

Required percentage = $\left(\dfrac{2}{8} \times 100\right)$%

$= \dfrac{200}{8}$%

= 25%

Hence, option 3 is the correct option.

10% of 10 + 20% of 20 - 30% of 30 is equal to:

1. 0

2. 9

3. -5

4. none of these

Answer

Solving,

$\Rightarrow \dfrac{10}{100} \times 10 + \dfrac{20}{100} \times 20 - \dfrac{30}{100} \times 30$

⇒ 1 + 4 - 9

⇒ -4

Since −4 is not among the given values,

Hence, option 4 is the correct option.

An article costing ₹ 60 one year ago now costs ₹ 40. The percentage change is:

1. $33\dfrac{1}{3}$% increase

2. $33\dfrac{1}{3}$% decrease

3. $133\dfrac{1}{3}$% decrease

4. $133\dfrac{1}{3}$% increase

Answer

Original cost = ₹ 60 and present cost = ₹ 40.

Since the cost has decreased, decrease = 60 − 40 = ₹ 20.

Percentage change = $\left(\dfrac{20}{60} \times 100\right)$%

$= \dfrac{2000}{60}$%

$= \dfrac{100}{3}$%

$= 33\dfrac{1}{3}$% decrease

Hence, option 2 is the correct option.

A is 80% of B, then B is:

1. 120% of A

2. 20% of A

3. 125% of A

4. 25% of A

Answer

Given, A = 80% of B = $\dfrac{80}{100}B = \dfrac{4}{5}B$.

$\Rightarrow B = \dfrac{5}{4}A\\[1em] \Rightarrow B = \left(\dfrac{5}{4} \times 100\right)$

Hence, option 3 is the correct option.

15% of a number is 30, then 20% of the same number is:

1. 60

2. 40

3. 36

4. 80

Answer

Let the number be x.

$\Rightarrow \dfrac{15}{100} \times x = 30\\[1em] \Rightarrow x = \dfrac{30 \times 100}{15}\\[1em] \Rightarrow x = 200$

Now, 20% of 200 = $\dfrac{20}{100} \times 200 = 40$.

Hence, option 2 is the correct option.

Rachna has to score 30% marks to pass an exam. She scored 140 marks and failed by 10 marks. The maximum marks are:

1. 70%

2. 150

3. 500

4. none of these

Answer

Marks scored = 140 and she failed by 10 marks.

Passing marks = 140 + 10 = 150.

Let the maximum marks be x. Since 30% of the maximum marks are needed to pass,

$\Rightarrow \dfrac{30}{100} \times x = 150\\[1em] \Rightarrow x = \dfrac{150 \times 100}{30}\\[1em] \Rightarrow x = 500$

Hence, option 3 is the correct option.

In a coaching institute, 40% are boys and 180 are girls. The total strength of the institute is:

1. 240

2. 220

3. 300

4. 350

Answer

Percentage of boys = 40%.

Percentage of girls = (100 − 40)% = 60%.

Let the total strength be x. Then 60% of x = 180.

$\Rightarrow \dfrac{60}{100} \times x = 180\\[1em] \Rightarrow x = \dfrac{180 \times 100}{60}\\[1em] \Rightarrow x = 300$

Hence, option 3 is the correct option.

A number increased by 20% becomes 720. The number is:

1. 500

2. 600

3. 800

4. 900

Answer

Let the number be x. When increased by 20%, it becomes 120% of x.

$\Rightarrow \dfrac{120}{100} \times x = 720\\[1em] \Rightarrow x = \dfrac{720 \times 100}{120}\\[1em] \Rightarrow x = 600$

Hence, option 2 is the correct option.

Peter bought a sweater and saved ₹ 40 when a discount of 20% was given. The price of the sweater after discount was:

1. ₹ 200

2. ₹ 240

3. ₹ 160

4. none of these

Answer

Let the marked price be ₹ x.

Given, 20% of x = ₹ 40 (saving).

$\Rightarrow \dfrac{20}{100} \times x = 40\\[1em] \Rightarrow x = \dfrac{40 \times 100}{20}\\[1em] \Rightarrow x = 200$

Price after discount = 200 − 40 = ₹ 160.

Hence, option 3 is the correct option.

The difference between 35% of a number and 20% of the same number is 300; the number is:

1. 2000

2. 4000

3. 3000

4. none of these

Answer

Let the number be x.

$\Rightarrow 35$

Hence, option 1 is the correct option.

Raj loses 20% of his salary. After spending 25% of the remainder, he has ₹ 2400 left. His salary is:

1. ₹ 6000

2. ₹ 4000

3. ₹ 1080

4. ₹ 5000

Answer

Let Raj's salary be ₹ x.

After losing 20%, remainder = (100 − 20)% of x = 80% of x = $\dfrac{4x}{5}$.

After spending 25% of the remainder, money left = (100 − 25)% of the remainder = 75% of $\dfrac{4x}{5}$.

$\Rightarrow \dfrac{75}{100} \times \dfrac{4x}{5} = 2400\\[1em] \Rightarrow \dfrac{3}{4} \times \dfrac{4x}{5} = 2400\\[1em] \Rightarrow \dfrac{3x}{5} = 2400\\[1em] \Rightarrow x = \dfrac{2400 \times 5}{3}\\[1em] \Rightarrow x = 4000$

Hence, option 2 is the correct option.

There are 100 boys and 100 girls in a school. If 10% of the boys and 20% of the girls leave the school, the percentage of students left is:

1. 70%

2. 85%

3. 15%

4. none of these

Answer

Total number of students = 100 + 100 = 200.

Boys who leave = 10% of 100 = 10.

Girls who leave = 20% of 100 = 20.

Total students who leave = 10 + 20 = 30.

Students left = 200 − 30 = 170.

Percentage of students left = $\left(\dfrac{170}{200} \times 100\right)$%

$= \dfrac{17000}{200}$%

= 85%

Hence, option 2 is the correct option.

Out of ₹ 400, a man loses 15% and spends one fifth of it. The money left with him is:

1. ₹ 140

2. ₹ 270

3. ₹ 272

4. ₹ 260

Answer

Total money = ₹ 400.

Money lost = 15% of 400 = $\dfrac{15}{100} \times 400 = ₹\ 60$.

Money spent = one fifth of 400 = $\dfrac{1}{5} \times 400 = ₹\ 80$.

Money left = ₹ (400 − 60 − 80) = ₹ 260.

Hence, option 4 is the correct option.

Number 45 is misread as 54. The percentage error is:

1. 120%

2. $83\dfrac{1}{3}$%

3. 20%

4. $16\dfrac{2}{3}$%

Answer

Actual number = 45 and misread number = 54.

Error = 54 − 45 = 9.

Percentage error = $\left(\dfrac{9}{45} \times 100\right)$%

$= \dfrac{900}{45}$%

= 20%

Hence, option 3 is the correct option.

A number reduced by 25% becomes 150. What percent should it be increased to become 250?

1. 20%

2. 25%

3. $16\dfrac{2}{3}$%

4. 50%

Answer

Let the number be x. When reduced by 25%, it becomes 75% of x.

$\Rightarrow \dfrac{75}{100} \times x = 150\\[1em] \Rightarrow x = \dfrac{150 \times 100}{75}\\[1em] \Rightarrow x = 200$

To become 250, increase needed = 250 − 200 = 50.

Percentage increase = $\left(\dfrac{50}{200} \times 100\right)$%

$= \dfrac{5000}{200}$%

= 25%

Hence, option 2 is the correct option.