Percent — Exercise 10(B)

Express:

₹ 5 as a percentage of ₹ 25.

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

$\Rightarrow \left(\dfrac{5}{25} \times 100\right)$%

$\Rightarrow \dfrac{500}{25}$%

⇒ 20%

Hence, ₹ 5 is 20% of ₹ 25.

Express:

80 paise as a percent of ₹ 4.

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

Converting ₹ 4 into paise :

₹ 4 = 4 × 100 paise = 400 paise.

$\Rightarrow \left(\dfrac{80}{400} \times 100\right)$%

$\Rightarrow \dfrac{8000}{400}$%

⇒ 20%

Hence, 80 paise is 20% of ₹ 4.

Express:

700 g as a percentage of 2.8 kg.

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

Converting 2.8 kg into grams :

2.8 kg = 2.8 × 1000 g = 2800 g.

$\Rightarrow \left(\dfrac{700}{2800} \times 100\right)$%

$\Rightarrow \dfrac{70000}{2800}$%

⇒ 25%

Hence, 700 g is 25% of 2.8 kg.

Express:

90 cm as a percent of 4.5 m.

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

Converting 4.5 m into centimetres :

4.5 m = 4.5 × 100 cm = 450 cm.

$\Rightarrow \left(\dfrac{90}{450} \times 100\right)$%

$\Rightarrow \dfrac{9000}{450}$%

⇒ 20%

Hence, 90 cm is 20% of 4.5 m.

Express the first quantity as a percent of the second:

40 p, ₹ 2

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

Converting ₹ 2 into paise :

₹ 2 = 2 × 100 p = 200 p.

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

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

⇒ 20%

Hence, 40 p is 20% of ₹ 2.

Express the first quantity as a percent of the second:

500 g, 6 kg

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

Converting 6 kg into grams :

6 kg = 6 × 1000 g = 6000 g.

$\Rightarrow \left(\dfrac{500}{6000} \times 100\right)$%

$\Rightarrow \dfrac{50000}{6000}$%

$\Rightarrow \dfrac{25}{3}$%

$\Rightarrow 8\dfrac{1}{3}$%

Hence, 500 g is $\mathbf{8\dfrac{1}{3}}$% of 6 kg.

Express the first quantity as a percent of the second:

42 seconds, 6 minutes.

Answer

To express one quantity as a percentage of another quantity, the two quantities must have the same unit. Then, divide the first quantity by the second one, multiply the result by 100 and write the percentage sign.

Converting 6 minutes into seconds :

6 minutes = 6 × 60 seconds = 360 seconds.

$\Rightarrow \left(\dfrac{42}{360} \times 100\right)$%

$\Rightarrow \dfrac{4200}{360}$%

$\Rightarrow \dfrac{35}{3}$%

$\Rightarrow 11\dfrac{2}{3}$%

Hence, 42 seconds is $\mathbf{11\dfrac{2}{3}}$% of 6 minutes.

Find the value of the following:

20% of ₹ 150

Answer

To find the percentage (percent) of a given quantity, express the given percent as a fraction and multiply it by the given quantity.

$\Rightarrow \dfrac{20}{100} \times ₹\ 150\\[1em] \Rightarrow ₹\ \dfrac{3{,}000}{100}\\[1em] \Rightarrow ₹\ 30$

Hence, 20% of ₹ 150 = ₹ 30.

Find the value of the following:

90% of 130

Answer

To find the percentage (percent) of a given quantity, express the given percent as a fraction and multiply it by the given quantity.

$\Rightarrow \dfrac{90}{100} \times 130\\[1em] \Rightarrow \dfrac{11700}{100}\\[1em] \Rightarrow 117$

Hence, 90% of 130 = 117.

Find the value of the following:

15% of 2 minutes

Answer

To find the percentage (percent) of a given quantity, express the given percent as a fraction and multiply it by the given quantity.

$\Rightarrow \dfrac{15}{100} \times 2 \text{ minutes}\\[1em] \Rightarrow \dfrac{30}{100} \text{ minutes}\\[1em] \Rightarrow 0.3 \text{ minutes}$

Converting 0.3 minutes into seconds :

0.3 minutes = 0.3 × 60 seconds = 18 seconds.

Hence, 15% of 2 minutes = 0.3 minutes = 18 seconds.

Find the value of the following:

7.5% of 500 kg.

Answer

To find the percentage (percent) of a given quantity, express the given percent as a fraction and multiply it by the given quantity.

$\Rightarrow \dfrac{7.5}{100} \times 500 \text{ kg}\\[1em] \Rightarrow \dfrac{3750}{100} \text{ kg}\\[1em] \Rightarrow 37.5 \text{ kg}$

Hence, 7.5% of 500 kg = 37.5 kg.

If a man spends 70% of his income, what percent does he save?

Answer

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

∴ Total income of the man = 100%.

Income spent by the man = 70%.

Percent of income saved = (100 − 70)% = 30%.

Hence, the man saves 30% of his income.

A girl gets 65 marks out of 80. What percentage of marks does she get?

Answer

Marks obtained by the girl = 65 and maximum marks = 80.

Percentage of marks = $\left(\dfrac{65}{80} \times 100\right)$%

= $\dfrac{6500}{80}$%

= $\dfrac{325}{4}$%

= $81\dfrac{1}{4}$%

= 81.25%

Hence, the percentage of marks obtained by the girl is $\mathbf{81\dfrac{1}{4}}$%, i.e., 81.25%.

A class contains 25 children, of which 6 are girls. What is the percentage of boys in the class?

Answer

Total number of children in the class = 25 and number of girls = 6.

Number of boys = 25 − 6 = 19.

Percentage of boys = $\left(\dfrac{19}{25} \times 100\right)$%

= $\dfrac{1900}{25}$%

= 76%

Hence, the percentage of boys in the class = 76%.

A tin contains 20 litres of petrol. Due to leakage, 3 litres of petrol is lost. What is the percentage of petrol left in the tin?

Answer

Total quantity of petrol in the tin = 20 litres and petrol lost = 3 litres.

Quantity of petrol left = 20 − 3 = 17 litres.

Percentage of petrol left = $\left(\dfrac{17}{20} \times 100\right)$%

= $\dfrac{1700}{20}$%

= 85%

Hence, the percentage of petrol left in the tin = 85%.

An alloy of copper and zinc contains 45% copper and the rest is zinc. Find the weight of zinc in 20 kg of the alloy.

Answer

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

Percentage of copper in the alloy = 45%.

∴ Percentage of zinc in the alloy = (100 − 45)% = 55%.

Weight of zinc in 20 kg of the alloy = 55% of 20 kg

= $\dfrac{55}{100} \times 20$ kg

= $\dfrac{1100}{100}$ kg

= 11 kg

Hence, the weight of zinc in 20 kg of the alloy = 11 kg.

A boy got 60 out of 80 in Hindi, 75 out of 100 in English, and 65 out of 70 in Arithmetic. In which subject is his percentage of marks the best? Also, find his overall percentage.

Answer

Percentage score in Hindi = $\left(\dfrac{60}{80} \times 100\right)$%

= $\dfrac{6000}{80}$%

= 75%.

Percentage score in English = $\left(\dfrac{75}{100} \times 100\right)$%

= $\dfrac{7500}{100}$%

= 75%.

Percentage score in Arithmetic = $\left(\dfrac{65}{70} \times 100\right)$%

= $\dfrac{6500}{70}$%

= $\dfrac{650}{7}$%

= $92\dfrac{6}{7}$% (= 92.86% approximately).

Since $92\dfrac{6}{7}$% > 75%, his percentage of marks is the best in Arithmetic.

For the overall percentage :

Sum of the maximum marks of all the three subjects = 80 + 100 + 70 = 250

and total score in the three subjects = 60 + 75 + 65 = 200.

Overall percentage = $\left(\dfrac{200}{250} \times 100\right)$%

= $\dfrac{20000}{250}$%

= 80%

Hence, the boy's percentage of marks is the highest in Arithmetic, i.e., $92\dfrac{6}{7}$% (approximately 92.86%), and his overall percentage is 80%.

60 more soldiers joined a camp of 500 soldiers. What percentage of the earlier soldiers do they make?

Answer

Number of soldiers earlier in the camp = 500 and number of soldiers who joined = 60.

Required percentage = $\left(\dfrac{60}{500} \times 100\right)$%

= $\dfrac{6000}{500}$%

= 12%

Hence, the soldiers who joined make 12% of the earlier soldiers.

In a plot of ground of area 6000 sq.m, only 4500 sq.m is allowed for construction. What percentage of area is to be left without construction?

Answer

Total area of the plot = 6000 sq.m and area allowed for construction = 4500 sq.m.

Area to be left without construction = 6000 − 4500 = 1500 sq.m.

Percentage of area left without construction = $\left(\dfrac{1500}{6000} \times 100\right)$%

= $\dfrac{150000}{6000}$%

= 25%

Hence, 25% of the area is to be left without construction.

Mr. Sharma has a monthly salary of ₹ 8,000. If he spends ₹ 6,400 every month, find:

(i) his monthly expenditure as percent.

(ii) his monthly savings as percent.

Answer

Monthly salary of Mr. Sharma = ₹ 8,000 and monthly expenditure = ₹ 6,400.

(i) Monthly expenditure as percent = $\left(\dfrac{6400}{8000} \times 100\right)$%

= $\dfrac{640000}{8000}$%

= 80%

Hence, his monthly expenditure is 80% of his salary.

(ii) Monthly savings = ₹ 8,000 − ₹ 6,400 = ₹ 1,600.

Monthly savings as percent = $\left(\dfrac{1600}{8000} \times 100\right)$%

= $\dfrac{160000}{8000}$%

= 20%

Hence, his monthly savings are 20% of his salary.

The monthly salary of Rohit is ₹ 24,000. If his salary increases by 12%, find his new monthly salary.

Answer

Original monthly salary of Rohit = ₹ 24,000.

Increase in salary = 12% of ₹ 24,000

= $\dfrac{12}{100} \times ₹\ 24{,}000$

= $₹\ \dfrac{2{,}88{,}000}{100}$

= ₹ 2,880

New monthly salary = ₹ 24,000 + ₹ 2,880 = ₹ 26,880.

Hence, the new monthly salary of Rohit = ₹ 26,880.

In a sale, the price of an article is reduced by 30%. If the original price of the article is ₹ 1,800, find:

(i) the reduction in the price of the article

(ii) the reduced price of the article.

Answer

Original price of the article = ₹ 1,800 and reduction = 30%.

(i) Reduction in the price = 30% of ₹ 1,800

= $\dfrac{30}{100} \times ₹\ 1{,}800$

= $₹\ \dfrac{54{,}000}{100}$

= ₹ 540

Hence, the reduction in the price of the article = ₹ 540.

(ii) Reduced price of the article = Original price − Reduction in price

= ₹ 1,800 − ₹ 540

= ₹ 1,260

Hence, the reduced price of the article = ₹ 1,260.

Evaluate:

30% of 200 + 20% of 450 - 25% of 600

Answer

Solving,

$\Rightarrow \dfrac{30}{100} \times 200 + \dfrac{20}{100} \times 450 - \dfrac{25}{100} \times 600$

⇒ 60 + 90 - 150

⇒ 150 - 150

⇒ 0

Hence, 30% of 200 + 20% of 450 − 25% of 600 = 0.

Evaluate:

10% of ₹ 450 - 12% of ₹ 500 + 8% of ₹ 500.

Answer

Solving,

$\Rightarrow \dfrac{10}{100} \times ₹\ 450 - \dfrac{12}{100} \times ₹\ 500 + \dfrac{8}{100} \times ₹\ 500$

⇒ ₹ 45 - ₹ 60 + ₹ 40

⇒ ₹ 85 - ₹ 60

⇒ ₹ 25

Hence, 10% of ₹ 450 − 12% of ₹ 500 + 8% of ₹ 500 = ₹ 25.