Percent and Percentage — Exercise 9(A)

Express the following as percent:

$\dfrac{3}{4}$

Answer

⇒ $\dfrac{3}{4}$

To convert a number into a percentage, multiply it by 100 and put the % sign.

⇒ $\left(\dfrac{3}{4} \times 100\right)$%

⇒ $\dfrac{300}{4}$%

⇒ 75%

Hence, $\dfrac{3}{4} = 75$%.

$\dfrac{2}{3}$

Answer

⇒ $\dfrac{2}{3}$

To convert a number into a percentage, multiply it by 100 and put the % sign.

⇒ $\left(\dfrac{2}{3} \times 100\right)$%

⇒ $\dfrac{200}{3}$%

⇒ $66\dfrac{2}{3}$%

Hence, $\dfrac{2}{3} = 66\dfrac{2}{3}$%.

0.025

Answer

⇒ 0.025

To convert a number into a percentage, multiply it by 100 and put the % sign.

⇒ 0.025 × 100%

⇒ 2.5%

Hence, 0.025 = 2.5%.

0.125

Answer

⇒ 0.125

To convert a number into a percentage, multiply it by 100 and put the % sign.

⇒ 0.125 × 100%

⇒ 12.5%

Hence, 0.125 = 12.5%.

Express the following percentage as fraction and as decimal number:

$7\dfrac{1}{2}$%

Answer

⇒ $7\dfrac{1}{2}$% = $\dfrac{15}{2}$%

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce to simplest form; the decimal is obtained from this fraction.

⇒ $\dfrac{15}{2}$%

$\Rightarrow \dfrac{15}{2} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{15}{200}\\[1em] \Rightarrow \dfrac{3}{40} \\[1em] \Rightarrow 0.075$

Hence, $7\dfrac{1}{2}$% = $\dfrac{3}{40}$ = 0.075.

2.50%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce to simplest form; the decimal is obtained from this fraction.

⇒ 2.50%

$\Rightarrow 2.50 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{2.5}{100}\\[1em] \Rightarrow \dfrac{25}{1000}\\[1em] \Rightarrow \dfrac{1}{40}$

As a decimal, $\dfrac{1}{40} = 0.025$.

Hence, 2.50% $= \dfrac{1}{40} = 0.025$.

0.02%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce to simplest form; the decimal is obtained from this fraction.

⇒ 0.02%

$\Rightarrow 0.02 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{0.02}{100}\\[1em] \Rightarrow \dfrac{2}{10000}\\[1em] \Rightarrow \dfrac{1}{5000}$

As a decimal, $\dfrac{1}{5000} = 0.0002$.

Hence, 0.02% $= \dfrac{1}{5000} = 0.0002$.

175%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce to simplest form; the decimal is obtained from this fraction.

⇒ 175%

$\Rightarrow 175 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{175}{100}\\[1em] \Rightarrow \dfrac{7}{4}\\[1em] \Rightarrow 1\dfrac{3}{4}$

As a decimal, $\dfrac{7}{4} = 1\dfrac{3}{4}= 1.75$.

Hence, 175% $= 1\dfrac{3}{4} = 1.75$.

What percent is:

16 hours of 2 days?

Answer

To express one quantity as a percent of another, both must be in the same units; then percentage = $\left(\dfrac{\text{one quantity}}{\text{other quantity}} \times 100\right)$%.

⇒ 16 hours of 2 days

We know, 1 day = 24 hours, so 2 days = 48 hours.

$\Rightarrow \left(\dfrac{16}{48} \times 100\right)$%

$\Rightarrow \dfrac{1600}{48}$%

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

$\Rightarrow 33\dfrac{1}{3}$%

Hence, 16 hours is $33\dfrac{1}{3}$% of 2 days.

40 paisa of ₹ 2?

Answer

To express one quantity as a percent of another, both must be in the same units; then percentage = $\left(\dfrac{\text{one quantity}}{\text{other quantity}} \times 100\right)$%.

⇒ 40 paisa of ₹ 2

We know, ₹ 1 = 100 paisa, so ₹ 2 = 200 paisa.

$\Rightarrow \left(\dfrac{40}{200} \times 100\right)$%

$\Rightarrow \dfrac{4000}{200}$%

$\Rightarrow 20$%

Hence, 40 paisa is 20% of ₹ 2.

25 cm of 4 metres?

Answer

To express one quantity as a percent of another, both must be in the same units; then percentage = $\left(\dfrac{\text{one quantity}}{\text{other quantity}} \times 100\right)$%.

⇒ 25 cm of 4 metres

We know, 1 m = 100 cm, so 4 m = 400 cm.

$\Rightarrow \left(\dfrac{25}{400} \times 100\right)$%

$\Rightarrow \dfrac{2500}{400}$%

$\Rightarrow \dfrac{25}{4}$%

$\Rightarrow 6\dfrac{1}{4}$%

Hence, 25 cm is $6\dfrac{1}{4}$% of 4 metres.

600 g of 5 kg?

Answer

To express one quantity as a percent of another, both must be in the same units; then percentage = $\left(\dfrac{\text{one quantity}}{\text{other quantity}} \times 100\right)$%.

⇒ 600 g of 5 kg

We know, 1 kg = 1000 g, so 5 kg = 5000 g.

$\Rightarrow \left(\dfrac{600}{5000} \times 100\right)$%

$\Rightarrow \dfrac{60000}{5000}$%

⇒ 12%

Hence, 600 g is 12% of 5 kg.

Find the value of:

5% of ₹ 350

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply by the given quantity.

⇒ 5% of ₹ 350

$\Rightarrow \dfrac{5}{100} \times 350\\[1em] \Rightarrow \dfrac{1750}{100}\\[1em] \Rightarrow ₹\ 17.50$

Hence, 5% of ₹ 350 = ₹ 17.50.

10% of ₹ 400.40

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply by the given quantity.

⇒ 10% of ₹ 400.40

$\Rightarrow \dfrac{10}{100} \times 400.40\\[1em] \Rightarrow \dfrac{4004}{100}\\[1em] \Rightarrow ₹\ 40.04$

Hence, 10% of ₹ 400.40 = ₹ 40.04.

1% of ₹ 500

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply by the given quantity.

⇒ 1% of ₹ 500

$\Rightarrow \dfrac{1}{100} \times 500$

⇒ ₹ 5

Hence, 1% of ₹ 500 = ₹ 5.

$12\dfrac{1}{2}$% of 80 kg

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply by the given quantity.

As, $12\dfrac{1}{2}$% = $\dfrac{25}{2}$%

⇒ $\dfrac{25}{2}$% of 80 kg

$\Rightarrow \dfrac{25}{2 \times 100} \times 80\\[1em] \Rightarrow \dfrac{25 \times 80}{200}\\[1em] \Rightarrow \dfrac{2000}{200}\\[1em] \Rightarrow 10 \text{ kg}$

Hence, $12\dfrac{1}{2}$% of 80 kg = 10 kg.

$\dfrac{5}{8}$% of ₹ 600

Answer

To find a percentage of a given quantity, change the percentage into a fraction and multiply by the given quantity.

⇒ $\dfrac{5}{8}$% of ₹ 600

$\Rightarrow \dfrac{5}{8 \times 100} \times 600\\[1em] \Rightarrow \dfrac{5 \times 600}{800}\\[1em] \Rightarrow \dfrac{3000}{800}\\[1em] \Rightarrow ₹\ 3.75$

Hence, $\dfrac{5}{8}$% of ₹ 600 = ₹ 3.75.

$33\dfrac{1}{3}$% of 27 m

Answer

⇒ $33\dfrac{1}{3}$% = $\dfrac{100}{3}$%

To find a percentage of a given quantity, change the percentage into a fraction and multiply by the given quantity.

⇒ $\dfrac{100}{3}$% of 27 m

$\Rightarrow \dfrac{100}{3 \times 100} \times 27\\[1em] \Rightarrow \dfrac{27}{3}\\[1em] \Rightarrow 9 \text{ m}$

Hence, $33\dfrac{1}{3}$% of 27 m = 9 m.

In a class of 60 children, 30% are girls. How many boys are there?

Answer

Total number of children = 60.

Percentage of girls = 30%.

Percentage of boys = (100 − 30)% = 70%.

Number of boys = 70% of 60

$= \dfrac{70}{100} \times 60\\[1em] = \dfrac{4200}{100}\\[1em] = 42$

Hence, there are 42 boys in the class.

In an election, two candidates A and B contested. A got 60% of the votes. The total votes polled were 8000. How many votes did each get?

Answer

Total votes polled = 8000.

Votes got by A = 60% of 8000

$= \dfrac{60}{100} \times 8000$

= 4800

Votes got by B = 8000 − 4800 = 3200.

Hence, A got 4800 votes and B got 3200 votes.

A person saves 12% of his salary every month. If his salary is ₹ 2,500, find his expenditure.

Answer

Total salary = ₹ 2,500.

Percentage saved = 12%.

Percentage of expenditure = (100 − 12)% = 88%.

Expenditure = 88% of 2,500

$= \dfrac{88}{100} \times 2,500\\[1em] = \dfrac{220000}{100}\\[1em] = ₹\ 2,200$

Hence, his expenditure = ₹ 2,200.

Seeta got 75% marks out of a total of 800. How many marks did she lose?

Answer

Total marks = 800.

Percentage of marks got = 75%.

Percentage of marks lost = (100 − 75)% = 25%.

Marks lost = 25% of 800

$= \dfrac{25}{100} \times 800$

= 200

Hence, Seeta lost 200 marks.

A shop worth ₹ 25,000 was insured for 95% of its value. How much would the owner get in case of any mishappening?

Answer

Value of the shop = ₹ 25,000.

Amount insured = 95% of 25,000

$= \dfrac{95}{100} \times 25,000\\[1em] = \dfrac{2375000}{100}\\[1em] = ₹\ 23,750$

Hence, the owner would get ₹ 23,750.

A class has 30 boys and 25 girls. What is the percentage of boys in the class?

Answer

Number of boys = 30 and number of girls = 25.

Total number of students = 30 + 25 = 55.

Percentage of boys = $\left(\dfrac{30}{55} \times 100\right)$%

$= \dfrac{3000}{55}$%

$= \dfrac{600}{11}$%

$= 54\dfrac{6}{11}$%

Hence, the percentage of boys in the class = $54\dfrac{6}{11}$%.

Express:

$3\dfrac{2}{5}$ as percent

Answer

$\Rightarrow 3\dfrac{2}{5} = \dfrac{17}{5}$

$\Rightarrow \dfrac{17}{5}$ as percent

$\Rightarrow \left(\dfrac{17}{5} \times 100\right)$%

$\Rightarrow \dfrac{1700}{5}$%

⇒ 340%

Hence, $3\dfrac{2}{5}$ = 340%.

0.0075 as percent

Answer

⇒ 0.0075 as percent

⇒ 0.0075 x 100%

⇒ 0.75%

Hence, 0.0075 = 0.75%.

3 : 20 as percent

Answer

⇒ 3 : 20 = $\dfrac{3}{20}$

$\Rightarrow \dfrac{3}{20}$ as percent

$\Rightarrow \left(\dfrac{3}{20} \times 100\right)$%

$\Rightarrow \dfrac{300}{20}$%

⇒ 15%

Hence, 3 : 20 = 15%.

60 cm as percent of 1 m 25 cm

Answer

⇒ 60 cm as percent of 1 m 25 cm

We know, 1 m 25 cm = 100 cm + 25 cm = 125 cm.

$\Rightarrow \left(\dfrac{60}{125} \times 100\right)$%

$\Rightarrow \dfrac{6000}{125}$%

⇒ 48%

Hence, 60 cm is 48% of 1 m 25 cm.

9 hours as percent of 4 days.

Answer

⇒ 9 hours as percent of 4 days

We know, 1 day = 24 hours, so 4 days = 96 hours.

$\Rightarrow \left(\dfrac{9}{96} \times 100\right)$%

$\Rightarrow \dfrac{900}{96}$%

$\Rightarrow \dfrac{75}{8}$%

$\Rightarrow 9\dfrac{3}{8}$%

⇒ 9.375 %

Hence, 9 hours is $9\dfrac{3}{8}$% = 9.375 % of 4 days.

Find 2% of 2 hours 30 min.

Answer

We know, 2 hours 30 min = (2 × 60 + 30) min = 150 min.

$\Rightarrow \dfrac{2}{100} \times 150\\[1em] \Rightarrow \dfrac{300}{100}\\[1em] \Rightarrow 3 \text{ min}$

Hence, 2% of 2 hours 30 min = 3 minutes.

What percent of 12 kg is 725 g?

Answer

We know, 1 kg = 1000 g, so 12 kg = 12000 g.

$\Rightarrow \left(\dfrac{725}{12000} \times 100\right)$%

$\Rightarrow \dfrac{72500}{12000}$%

$\Rightarrow \dfrac{145}{24}$%

$\Rightarrow 6\dfrac{1}{24}$%

Hence, 725 g is $6\dfrac{1}{24}$% of 12 kg.