Percent

To express a statement in the percentage form, write it as a fraction and then multiply the fraction by 100 and write the percentage sign.

⇒ 13 out of 20

$\Rightarrow \frac{13}{20}$

$\Rightarrow \left(\frac{13}{20} \times 100\right)$%

$\Rightarrow \frac{1300}{20}$%

⇒ 65%

Hence, 13 out of 20 = 65%.

To express a statement in the percentage form, write it as a fraction and then multiply the fraction by 100 and write the percentage sign.

⇒ 21 eggs out of 30 are good

$\Rightarrow \frac{21}{30}$ eggs are good

$\Rightarrow \left(\frac{21}{30} \times 100\right)$% eggs are good

$\Rightarrow \frac{2100}{30}$% eggs are good

⇒ 70% eggs are good

Hence, 70% of the eggs are good.

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\frac{3}{200} \times 100\right)$%

$\Rightarrow \frac{300}{200}$%

$\Rightarrow \frac{3}{2}$%

⇒ 1.5%

Hence, $\mathbf{\frac{3}{200} = 1.5}$%.

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\frac{5}{6} \times 100\right)$%

$\Rightarrow \frac{500}{6}$%

$\Rightarrow \frac{250}{3}$%

$\Rightarrow 83\frac{1}{3}$%

Hence, $\mathbf{\frac{5}{6} = 83\frac{1}{3}}$%.

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\frac{65}{80} \times 100\right)$%

$\Rightarrow \frac{6500}{80}$%

$\Rightarrow \frac{325}{4}$%

$\Rightarrow 81\frac{1}{4}$% = 81.25%

Hence, $\mathbf{\frac{65}{80} = 81\frac{1}{4}}$% = 81.25%.

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\frac{2}{3} \times 100\right)$%

$\Rightarrow \frac{200}{3}$%

$\Rightarrow 66\frac{2}{3}$%

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

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.10 × 100)%

⇒ 10%

Hence, 0.10 = 10%.

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.02 × 100)%

⇒ 2%

Hence, 0.02 = 2%.

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.7 × 100)%

⇒ 70%

Hence, 0.7 = 70%.

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.15 × 100)%

⇒ 15%

Hence, 0.15 = 15%.

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.032 × 100)%

⇒ 3.2%

Hence, 0.032 = 3.2%.

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \frac{8}{100}$

$\Rightarrow \frac{2}{25}$

Hence, 8% = $\mathbf{\frac{2}{25}}$.

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \frac{20}{100}$

$\Rightarrow \frac{1}{5}$

Hence, 20% = $\mathbf{\frac{1}{5}}$.

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \frac{85}{100}$

$\Rightarrow \frac{17}{20}$

Hence, 85% = $\mathbf{\frac{17}{20}}$.

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$$\begin{aligned}\Rightarrow \frac{250}{100} \\[1em] \Rightarrow \frac{5}{2} \\[1em] \Rightarrow 2\frac{1}{2}\end{aligned}$$

Hence, 250% = $\mathbf{\frac{5}{2} = 2\frac{1}{2}}$.

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow 12\frac{1}{2}$% = $\frac{25}{2}$%

$\Rightarrow \frac{25}{2} \times \frac{1}{100}$

$\Rightarrow \frac{25}{200}$

$\Rightarrow \frac{1}{8}$

Hence, $\mathbf{12\frac{1}{2}}$% = $\mathbf{\frac{1}{8}}$.

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \frac{25}{100}$

⇒ 0.25

Hence, 25% = 0.25.

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \frac{108}{100}$

⇒ 1.08

Hence, 108% = 1.08.

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \frac{95}{100}$

⇒ 0.95

Hence, 95% = 0.95.

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \frac{4.5}{100}$

⇒ 0.045

Hence, 4.5% = 0.045.

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \frac{29.2}{100}$

⇒ 0.292

Hence, 29.2% = 0.292.

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (7 × 100)%

⇒ 700%

Hence, 7 expressed as a percent is 700%.

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (2 × 100)%

⇒ 200%

Hence, 2 expressed as a percent is 200%.

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (19.5 × 100)%

⇒ 1950%

Hence, 19.5 expressed as a percent is 1950%.

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (5.37 × 100)%

⇒ 537%

Hence, 5.37 expressed as a percent is 537%.

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.

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

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

⇒ 20%

Hence, ₹ 5 is 20% of ₹ 25.

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.

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

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

⇒ 20%

Hence, 80 paise is 20% of ₹ 4.

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.

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

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

⇒ 25%

Hence, 700 g is 25% of 2.8 kg.

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.

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

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

⇒ 20%

Hence, 90 cm is 20% of 4.5 m.

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.

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

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

⇒ 20%

Hence, 40 p is 20% of ₹ 2.

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.

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

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

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

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

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

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.

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

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

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

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

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

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

$$\begin{aligned}\Rightarrow \frac{20}{100} \times ₹\ 150\\[1em] \Rightarrow ₹\ \frac{3{,}000}{100}\\[1em] \Rightarrow ₹\ 30\end{aligned}$$

Hence, 20% of ₹ 150 = ₹ 30.

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

$$\begin{aligned}\Rightarrow \frac{90}{100} \times 130\\[1em] \Rightarrow \frac{11700}{100}\\[1em] \Rightarrow 117\end{aligned}$$

Hence, 90% of 130 = 117.

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

$$\begin{aligned}\Rightarrow \frac{15}{100} \times 2 \text{ minutes}\\[1em] \Rightarrow \frac{30}{100} \text{ minutes}\\[1em] \Rightarrow 0.3 \text{ minutes}\end{aligned}$$

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.

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

$$\begin{aligned}\Rightarrow \frac{7.5}{100} \times 500 \text{ kg}\\[1em] \Rightarrow \frac{3750}{100} \text{ kg}\\[1em] \Rightarrow 37.5 \text{ kg}\end{aligned}$$

Hence, 7.5% of 500 kg = 37.5 kg.

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.

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

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

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

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

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

= 81.25%

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

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

Number of boys = 25 − 6 = 19.

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

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

= 76%

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

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 = $\left(\frac{17}{20} \times 100\right)$%

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

= 85%

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

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

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

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

= 11 kg

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

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

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

= 75%.

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

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

= 75%.

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

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

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

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

Since $92\frac{6}{7}$% > 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 = $\left(\frac{200}{250} \times 100\right)$%

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

= 80%

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

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

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

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

= 12%

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

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 = $\left(\frac{1500}{6000} \times 100\right)$%

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

= 25%

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

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

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

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

= 80%

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

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

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

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

= 20%

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

Original monthly salary of Rohit = ₹ 24,000.

Increase in salary = 12% of ₹ 24,000

= $\frac{12}{100} \times ₹\ 24{,}000$

= $₹\ \frac{2{,}88{,}000}{100}$

= ₹ 2,880

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

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

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

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

= $\frac{30}{100} \times ₹\ 1{,}800$

= $₹\ \frac{54{,}000}{100}$

= ₹ 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.

Solving,

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

⇒ 60 + 90 - 150

⇒ 150 - 150

⇒ 0

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

Solving,

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

⇒ ₹ 45 - ₹ 60 + ₹ 40

⇒ ₹ 85 - ₹ 60

⇒ ₹ 25

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

Original price of rice = ₹ 30 per kg and new price of rice = ₹ 36 per kg.

Increase in price = ₹ 36 − ₹ 30 = ₹ 6.

Increase % = $\left(\frac{\text{Increase in price}}{\text{Original price}} \times 100\right)$%

= $\left(\frac{6}{30} \times 100\right)$%

= $\frac{600}{30}$%

= 20%

Hence, the percentage rise in the price of rice = 20%.

Original population (in 1979) = 4000 and new population (in 1981) = 4500.

Increase in population = 4500 − 4000 = 500.

Increase % = $\left(\frac{\text{Increase in population}}{\text{Original population}} \times 100\right)$%

= $\left(\frac{500}{4000} \times 100\right)$%

= $\frac{50000}{4000}$%

= $\frac{25}{2}$%

= 12.5%

Hence, the population had increased by 12.5%.

Original price of the scooter = ₹ 8,000 and new price = ₹ 6,000.

Decrease in price = ₹ 8,000 − ₹ 6,000 = ₹ 2,000.

Decrease % = $\left(\frac{\text{Decrease in price}}{\text{Original price}} \times 100\right)$%

= $\left(\frac{2000}{8000} \times 100\right)$%

= $\frac{200000}{8000}$%

= 25%

Hence, the price of the scooter came down by 25%.

Decrease in it = 8% of ₹ 400

= $\frac{8}{100} \times ₹\ 400$

= $₹\ \frac{3{,}200}{100}$

= ₹ 32

Decreased quantity = ₹ 400 − ₹ 32 = ₹ 368.

Hence, the resulting quantity = ₹ 368.

Increase in it = 5% of 25 km

= $\frac{5}{100} \times 25$ km

= $\frac{125}{100}$ km

= 1.25 km

Increased quantity = 25 km + 1.25 km = 26.25 km.

Hence, the resulting quantity = 26.25 km.

Here, $12\frac{1}{2}$% = $\frac{25}{2}$%.

Increase in it = $\frac{25}{2}$% of 600 km h^-1

= $\frac{25}{2 \times 100} \times 600$ km h^-1

= $\frac{15000}{200}$ km h^-1

= 75 km h^-1

Increased speed = 600 km h^-1 + 75 km h^-1 = 675 km h^-1 = 675 km/h.

Hence, the resulting quantity = 675 km/h.

Increase in it = 2.5% of ₹ 62,500

= $\frac{2.5}{100} \times ₹\ 62{,}500$

= $₹\ \frac{1{,}56{,}250}{100}$

= ₹ 1,562.50

Increased salary = ₹ 62,500 + ₹ 1,562.50 = ₹ 64,062.50.

Hence, the resulting quantity = ₹ 64,062.50.

Original population of the village = 25,000 and decrease = 12%.

Decrease in population = 12% of 25,000

= $\frac{12}{100} \times 25{,}000$

= $\frac{300000}{100}$

= 3,000

Population after the decrease = 25,000 − 3,000 = 22,000.

Hence, the population after the decrease = 22,000.

Total salary = ₹ 13,500.

Savings = $\frac{1}{3}$ of ₹ 13,500 $= ₹\ \frac{13{,}500}{3} = ₹\ 4{,}500$.

Remaining money = ₹ 13,500 − ₹ 4,500 = ₹ 9,000.

Money spent on food = 50% of ₹ 9,000

= $\frac{50}{100} \times ₹\ 9{,}000$

= $₹\ \frac{4{,}50{,}000}{100}$

= ₹ 4,500

Money spent on house rent = 20% of ₹ 9,000

= $\frac{20}{100} \times ₹\ 9{,}000$

= $₹\ \frac{1{,}80{,}000}{100}$

= ₹ 1,800

Money spent on both = ₹ 4,500 + ₹ 1,800 = ₹ 6,300.

Hence, ₹ 4,500 is spent on food, ₹ 1,800 is spent on house rent and ₹ 6,300 is spent in total on both food and rent.

Total capacity of the tank = 50 litres.

Water present in the tank = 30% of 50 litres

= $\frac{30}{100} \times 50$ litres

= $\frac{1500}{100}$ litres

= 15 litres

Water required to make the tank 50% full = 50% of 50 litres

= $\frac{50}{100} \times 50$ litres

= $\frac{2500}{100}$ litres

= 25 litres

Water to be put into the tank = 25 litres − 15 litres = 10 litres.

Hence, 10 litres of water should be put into the tank.

Total number of voters = 80,000.

Number of voters who went to the polls = 80% of 80,000

= $\frac{80}{100} \times 80{,}000$

= $\frac{6400000}{100}$

= 64,000

Since 60% of these voters vote for A, the remaining (100 − 60)% = 40% vote for B.

Number of votes B gets = 40% of 64,000

= $\frac{40}{100} \times 64{,}000$

= $\frac{2560000}{100}$

= 25,600

Hence, B gets 25,600 votes.

Body weight of the person = 56 kg and water content = 70% of the body weight.

Weight of water in the body = 70% of 56 kg

= $\frac{70}{100} \times 56$ kg

= $\frac{3920}{100}$ kg

= 39.2 kg

Hence, the weight of water in the body of the person = 39.2 kg.

(i) Water available in liquid form = $\frac{1}{5}$ of the available water.

Percentage of water available in liquid form = $\left(\frac{1}{5} \times 100\right)$%

= $\frac{100}{5}$%

= 20%

Hence, the water available in liquid form = 20%.

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

Percentage of water available in frozen form = (100 − 20)% = 80%.

Hence, the water available in frozen form = 80%.

(i) Weight of water in 25 kg of tomato = 90% of 25 kg

= $\frac{90}{100} \times 25$ kg

= $\frac{2250}{100}$ kg

= 22.5 kg

Hence, the weight of water in 25 kg of tomato = 22.5 kg.

(ii) Weight of water in 90 kg of potato = 78% of 90 kg

= $\frac{78}{100} \times 90$ kg

= $\frac{7020}{100}$ kg

= 70.2 kg

Weight of water in 30 kg of tomato = 90% of 30 kg

= $\frac{90}{100} \times 30$ kg

= $\frac{2700}{100}$ kg

= 27 kg

Total quantity of water = 70.2 kg + 27 kg = 97.2 kg.

Hence, the total quantity, by weight, of water = 97.2 kg.

Increase in it = 50% of 48

= $\frac{50}{100} \times 48$

= $\frac{2400}{100}$

= 24

Required number = 48 + 24 = 72.

Hence, the number that is 50% more than 48 = 72.

Decrease in it = 30% of 70

= $\frac{30}{100} \times 70$

= $\frac{2100}{100}$

= 21

Required number = 70 − 21 = 49.

Hence, the number that is 30% less than 70 = 49.

$\Rightarrow \frac{8}{100} \times 900 - \frac{12}{100} \times 750 + \frac{20}{100} \times 165$

⇒ 72 - 90 + 33

⇒ 105 - 90

⇒ 15

Hence, 8% of 900 − 12% of 750 + 20% of 165 = 15.

$\Rightarrow \frac{70}{100} \times 70 + \frac{90}{100} \times 90 - \frac{120}{100} \times 120$

⇒ 49 + 81 - 144

⇒ 130 - 144

⇒ -14

Hence, 70% of 70 + 90% of 90 − 120% of 120 = −14.

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

Percentage of water not fit for drinking = 97.3%.

Percentage of water fit for drinking = (100 − 97.3)% = 2.7%.

Hence, the percentage of water on the earth that is fit for drinking = 2.7%.

(ii) Let the total volume of water available be $x$ m³.

Since 2.7% of the water is fit for drinking,

$$\begin{aligned}\Rightarrow \frac{2.7}{100} \times x = 21{,}600\\[1em] \Rightarrow x = \frac{21{,}600 \times 100}{2.7}\\[1em] \Rightarrow x = \frac{21{,}60{,}000}{2.7}\\[1em] \Rightarrow x = 8{,}00{,}000\end{aligned}$$

Hence, the total volume of water available = 8,00,000 m³.

Total quantity of air = 800 m³.

Quantity of nitrogen = 78% of 800 m³

= $\frac{78}{100} \times 800$ m³

= $\frac{62400}{100}$ m³

= 624 m³

Quantity of oxygen = 21% of 800 m³

= $\frac{21}{100} \times 800$ m³

= $\frac{16800}{100}$ m³

= 168 m³

Quantity of other gases = 1% of 800 m³

= $\frac{1}{100} \times 800$ m³

= $\frac{800}{100}$ m³

= 8 m³

Hence, nitrogen = 624 m³, oxygen = 168 m³ and other gases = 8 m³.

To convert a decimal into percentage, multiply it by 100 and write the sign of percentage.

⇒ (0.75 × 100)%

⇒ 75%

Hence, option 2 is the correct option.

Writing the ratio 4 : 5 as a fraction and then multiplying the fraction by 100 and writing the percentage sign :

⇒ 4 : 5

$\Rightarrow \frac{4}{5}$

$\Rightarrow \left(\frac{4}{5} \times 100\right)$%

$\Rightarrow \frac{400}{5}$%

⇒ 80%

Hence, option 1 is the correct option.

The given quantity is in kilogram, whereas all the options are in gram. So, 2 kg is first converted into gram, as the answer and the options must be in the same unit.

Converting 2 kg into grams :

2 kg = 2 × 1000 g = 2000 g.

80% of 2000 g

$$\begin{aligned}\Rightarrow \frac{80}{100} \times 2000 \text{ g}\\[1em] \Rightarrow \frac{160000}{100} \text{ g}\\[1em] \Rightarrow 1600 \text{ g}\end{aligned}$$

Hence, option 1 is the correct option.

⇒ 40% of 400

$$\begin{aligned}\Rightarrow \frac{40}{100} \times 400\\[1em] \Rightarrow \frac{16000}{100}\\[1em] \Rightarrow 160\end{aligned}$$

∴ 400 − 40% of 400 = 400 − 160 = 240.

Hence, option 2 is the correct option.

⇒ 80% of 500 − 30% of 500

$\Rightarrow \frac{80}{100} \times 500 - \frac{30}{100} \times 500$

⇒ 400 - 150

⇒ 250

Hence, option 3 is the correct option.

The increase is 50% of 800.

$$\begin{aligned}\Rightarrow \frac{50}{100} \times 800\\[1em] \Rightarrow \frac{40000}{100}\\[1em] \Rightarrow 400\end{aligned}$$

Hence, option 2 is the correct option.

Decrease in it = 25% of 1600

= $\frac{25}{100} \times 1600$

= $\frac{40000}{100}$

= 400

Decreased number = 1600 − 400 = 1200.

Hence, option 1 is the correct option.

Increase in it = 50% of 80

= $\frac{50}{100} \times 80$

= $\frac{4000}{100}$

= 40

Increased number = 80 + 40 = 120.

Hence, option 4 is the correct option.

Decrease in it = 20% of 500

= $\frac{20}{100} \times 500$

= $\frac{10000}{100}$

= 100

Decreased number = 500 − 100 = 400.

Hence, option 3 is the correct option.

⇒ 50% of 20 − 20% of 50

$\Rightarrow \frac{50}{100} \times 20 - \frac{20}{100} \times 50$

⇒ 10 - 10

⇒ 0

Hence, option 3 is the correct option.

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

Number of boys = 60% of 1000

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

= $\frac{60000}{100}$

= 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.

Solving,

⇒ 10% of 600 + 15% of 600

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

⇒ 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

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

⇒ 150

Thus, statement 2 is true.

Hence, option 1 is the correct option.

40% of 800 $= \frac{40}{100} \times 800 = 320$.

∴ 800 − 40% of 800 = 800 − 320 = 480, and not 240.

Thus, Assertion (A) is false.

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

⇒ 800 - 40% of 800

⇒ (100 - 40)% of 800

⇒ 60% of 800

Thus, Reason (R) is true.

Hence, option 2 is the correct option.

Original value = 300 and new value = 390.

Increase in value = 390 − 300 = 90.

⇒ Increase% = $\left(\frac{90}{300} \times 100\right)$%

⇒ Increase% = $\frac{9000}{300}$%

⇒ Increase% = 30%

Thus, Assertion (A) is true.

The formula to find the increase percent is

Increase% = $\frac{\text{Increase in value}}{\text{Original value}} \times 100$%, which is correct.

Thus, Reason (R) is true.

Hence, option 3 is the correct option.