Percentage

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 8%

$$\begin{aligned}\Rightarrow 8 \times \frac{1}{100}\\[1em] \Rightarrow \frac{8}{100}\\[1em] \Rightarrow \frac{2}{25}\end{aligned}$$

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

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 36%

$$\begin{aligned}\Rightarrow 36 \times \frac{1}{100}\\[1em] \Rightarrow \frac{36}{100}\\[1em] \Rightarrow \frac{9}{25}\end{aligned}$$

Hence, 36% = $\mathbf{\frac{9}{25}}$.

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 125%

$$\begin{aligned}\Rightarrow 125 \times \frac{1}{100}\\[1em] \Rightarrow \frac{125}{100}\\[1em] \Rightarrow \frac{5}{4}\end{aligned}$$

Hence, 125% = $\mathbf{\frac{5}{4}}$.

⇒ $12\frac{1}{2}$% = $\frac{25}{2}$%

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

$$\begin{aligned}\Rightarrow \frac{25}{2} \times \frac{1}{100}\\[1em] \Rightarrow \frac{25}{200}\\[1em] \Rightarrow \frac{1}{8}\end{aligned}$$

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

⇒ $26\frac{2}{3}$% = $\frac{80}{3}$%

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

$$\begin{aligned}\Rightarrow \frac{80}{3} \times \frac{1}{100}\\[1em] \Rightarrow \frac{80}{300}\\[1em] \Rightarrow \frac{4}{15}\end{aligned}$$

Hence, $\mathbf{26\frac{2}{3}}$% = $\mathbf{\frac{4}{15}}$.

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 9.6%

$$\begin{aligned}\Rightarrow 9.6 \times \frac{1}{100}\\[1em] \Rightarrow \frac{9.6}{100}\\[1em] \Rightarrow \frac{96}{1000}\\[1em] \Rightarrow \frac{12}{125}\end{aligned}$$

Hence, 9.6% = $\mathbf{\frac{12}{125}}$.

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 0.36%

$$\begin{aligned}\Rightarrow 0.36 \times \frac{1}{100}\\[1em] \Rightarrow \frac{0.36}{100}\\[1em] \Rightarrow \frac{36}{10000}\\[1em] \Rightarrow \frac{9}{2500}\end{aligned}$$

Hence, 0.36% = $\mathbf{\frac{9}{2500}}$.

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ $\frac{4}{5}$%

$$\begin{aligned}\Rightarrow \frac{4}{5} \times \frac{1}{100}\\[1em] \Rightarrow \frac{4}{500}\\[1em] \Rightarrow \frac{1}{125}\end{aligned}$$

Hence, $\mathbf{\frac{4}{5}}$% = $\mathbf{\frac{1}{125}}$.

To convert a percentage into a decimal, replace the % sign with $\frac{1}{100}$ and express the fraction as a decimal.

⇒ 43%

$$\begin{aligned}\Rightarrow 43 \times \frac{1}{100}\\[1em] \Rightarrow \frac{43}{100}\\[1em] \Rightarrow 0.43\end{aligned}$$

Hence, 43% = 0.43.

To convert a percentage into a decimal, replace the % sign with $\frac{1}{100}$ and express the fraction as a decimal.

⇒ 7%

$$\begin{aligned}\Rightarrow 7 \times \frac{1}{100}\\[1em] \Rightarrow \frac{7}{100}\\[1em] \Rightarrow 0.07\end{aligned}$$

Hence, 7% = 0.07.

To convert a percentage into a decimal, replace the % sign with $\frac{1}{100}$ and express the fraction as a decimal.

⇒ 120%

$$\begin{aligned}\Rightarrow 120 \times \frac{1}{100}\\[1em] \Rightarrow \frac{120}{100}\\[1em] \Rightarrow 1.2\end{aligned}$$

Hence, 120% = 1.2.

To convert a percentage into a decimal, replace the % sign with $\frac{1}{100}$ and express the fraction as a decimal.

⇒ 3.5%

$$\begin{aligned}\Rightarrow 3.5 \times \frac{1}{100}\\[1em] \Rightarrow \frac{3.5}{100}\\[1em] \Rightarrow 0.035\end{aligned}$$

Hence, 3.5% = 0.035.

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

⇒ 56%

$$\begin{aligned}\Rightarrow 56 \times \frac{1}{100}\\[1em] \Rightarrow \frac{56}{100}\\[1em] \Rightarrow \frac{14}{25}\\[1em] \Rightarrow 14 : 25\end{aligned}$$

Hence, 56% = 14 : 25.

⇒ $16\frac{2}{3}$% = $\frac{50}{3}$%

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

$$\begin{aligned}\Rightarrow \frac{50}{3} \times \frac{1}{100}\\[1em] \Rightarrow \frac{50}{300}\\[1em] \Rightarrow \frac{1}{6}\\[1em] \Rightarrow 1 : 6\end{aligned}$$

Hence, $\mathbf{16\frac{2}{3}}$% = 1 : 6.

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

⇒ 6.4%

$$\begin{aligned}\Rightarrow 6.4 \times \frac{1}{100}\\[1em] \Rightarrow \frac{6.4}{100}\\[1em] \Rightarrow \frac{64}{1000}\\[1em] \Rightarrow \frac{8}{125}\\[1em] \Rightarrow 8 : 125\end{aligned}$$

Hence, 6.4% = 8 : 125.

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

⇒ 0.8%

$$\begin{aligned}\Rightarrow 0.8 \times \frac{1}{100}\\[1em] \Rightarrow \frac{0.8}{100}\\[1em] \Rightarrow \frac{8}{1000}\\[1em] \Rightarrow \frac{1}{125}\\[1em] \Rightarrow 1 : 125\end{aligned}$$

Hence, 0.8% = 1 : 125.

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$; the fraction may then be written as a decimal or a ratio, as desired.

(i) As a fraction:

⇒ 15%

$\Rightarrow \frac{15}{100}$

$\Rightarrow \frac{3}{20}$

Hence, 15% as a fraction = $\mathbf{\frac{3}{20}}$.

(ii) As a decimal:

⇒ 15%

$\Rightarrow \frac{15}{100}$

$\Rightarrow 0.15$

Hence, 15% as a decimal = 0.15

(iii) As a ratio:

⇒ 15%

$\Rightarrow \frac{15}{100}$

$\Rightarrow \frac{3}{20}$

⇒ 3 : 20

Hence, 15% as a ratio = 3 : 20.

To convert a percentage into a fraction, replace the % sign with $\frac{1}{100}$; the fraction may then be written as a decimal or a ratio, as desired.

(i) As a fraction:

⇒ 136%

$\Rightarrow \frac{136}{100}$

$\Rightarrow \frac{34}{25}$

Hence, 136% as a fraction = $\mathbf{\frac{34}{25}}$.

(ii) As a decimal:

⇒ 136%

$\Rightarrow \frac{136}{100}$

$\Rightarrow \frac{34}{25}$

$\Rightarrow 1.36$

Hence, 136% as a decimal = 1.36

(iii) As a ratio:

⇒ 136%

$\Rightarrow \frac{136}{100}$

$\Rightarrow \frac{34}{25}$

$\Rightarrow 34 : 25$

Hence, 136% as a ratio = 34 : 25.

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

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

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

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

$\Rightarrow 65$%

Hence, $\mathbf{\frac{13}{20}}$ = 65%.

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

$\Rightarrow \frac{7}{16}$

$\Rightarrow \left(\frac{7}{16} \times 100\right)$%

$\Rightarrow \frac{700}{16}$%

$\Rightarrow \frac{175}{4}$%

$\Rightarrow 43\frac{3}{4}$%

Hence, $\mathbf{\frac{7}{16}}$ = $\mathbf{43\frac{3}{4}}$%.

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

$\Rightarrow \frac{5}{12}$

$\Rightarrow \left(\frac{5}{12} \times 100\right)$%

$\Rightarrow \frac{500}{12}$%

$\Rightarrow \frac{125}{3}$%

$\Rightarrow 41\frac{2}{3}$%

Hence, $\mathbf{\frac{5}{12}}$ = $\mathbf{41\frac{2}{3}}$%.

⇒ $2\frac{3}{4} = \frac{11}{4}$

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

$\Rightarrow \left(\frac{11}{4} \times 100\right)$%

$\Rightarrow \frac{1100}{4}$%

$\Rightarrow 275$%

Hence, $\mathbf{2\frac{3}{4}}$ = 275%.

⇒ $1\frac{7}{8} = \frac{15}{8}$

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

$\Rightarrow \left(\frac{15}{8} \times 100\right)$%

$\Rightarrow \frac{1500}{8}$%

$\Rightarrow \frac{375}{2}$%

$\Rightarrow 187\frac{1}{2}$%

Hence, $\mathbf{1\frac{7}{8}}$ = $\mathbf{187\frac{1}{2}}$%.

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

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

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

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

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

$\Rightarrow 1\frac{1}{2}$%

Hence, $\mathbf{\frac{3}{200}}$ = $\mathbf{1\frac{1}{2}}$%.

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

$\Rightarrow \frac{24}{5}$

$\Rightarrow \left(\frac{24}{5} \times 100\right)$%

$\Rightarrow \frac{2400}{5}$%

$\Rightarrow 480$%

Hence, $\mathbf{\frac{24}{5}}$ = 480%.

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

$\Rightarrow 3$

$\Rightarrow (3 \times 100)$%

$\Rightarrow 300$%

Hence, 3 = 300%.

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

⇒ 0.7

⇒ (0.7 × 100)%

⇒ 70%

Hence, 0.7 = 70%.

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

⇒ 0.54

⇒ (0.54 × 100)%

⇒ 54%

Hence, 0.54 = 54%.

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

⇒ 0.06

⇒ (0.06 × 100)%

⇒ 6%

Hence, 0.06 = 6%.

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

⇒ 0.073

⇒ (0.073 × 100)%

⇒ 7.3%

Hence, 0.073 = 7.3%.

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

⇒ 2.05

⇒ (2.05 × 100)%

⇒ 205%

Hence, 2.05 = 205%.

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

⇒ 4.3

⇒ (4.3 × 100)%

⇒ 430%

Hence, 4.3 = 430%.

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

⇒ 1.065

$\Rightarrow \Big(\frac{1065}{1000} \times 100\Big)$%

$\Rightarrow 106\frac{1}{2}$%

Hence, 1.065 = $\mathbf{106\frac{1}{2}}$%.

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

⇒ 0.005 or $\frac{5}{1000}$

$\Rightarrow \Big(\frac{5}{1000} \times 100 \Big)$%

$\Rightarrow \frac{1}{2}$%

Hence, 0.005 = $\mathbf{\frac{1}{2}}$%.

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

⇒ 16% of 175

$$\begin{aligned}\Rightarrow \frac{16}{100} \times 175\\[1em] \Rightarrow \frac{2800}{100}\\[1em] \Rightarrow 28\end{aligned}$$

Hence, 16% of 175 = 28.

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

⇒ 140% of 45

$$\begin{aligned}\Rightarrow \frac{140}{100} \times 45\\[1em] \Rightarrow \frac{6300}{100}\\[1em] \Rightarrow 63\end{aligned}$$

Hence, 140% of 45 = 63.

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

⇒ 2% of 120

$$\begin{aligned}\Rightarrow \frac{2}{100} \times 120\\[1em] \Rightarrow \frac{240}{100}\\[1em] \Rightarrow 2.4\end{aligned}$$

Hence, 2% of 120 = 2.4.

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

⇒ 12.5% of 72

$$\begin{aligned}\Rightarrow \frac{12.5}{100} \times 72\\[1em] \Rightarrow \frac{900}{100}\\[1em] \Rightarrow 9\end{aligned}$$

Hence, 12.5% of 72 = 9.

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

⇒ 14% of 14

$$\begin{aligned}\Rightarrow \frac{14}{100} \times 14\\[1em] \Rightarrow \frac{196}{100}\\[1em] \Rightarrow 1.96\end{aligned}$$

Hence, 14% of 14 = 1.96.

⇒ $16\frac{2}{3}$% = $\frac{50}{3}$%

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

⇒ $\frac{50}{3}$% of 18

$$\begin{aligned}\Rightarrow \frac{50}{3 \times 100} \times 18\\[1em] \Rightarrow \frac{50 \times 18}{300}\\[1em] \Rightarrow \frac{900}{300}\\[1em] \Rightarrow 3\end{aligned}$$

Hence, $\mathbf{16\frac{2}{3}}$% of 18 = 3.

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

⇒ 5% of 12.6

$$\begin{aligned}\Rightarrow \frac{5}{100} \times 12.6\\[1em] \Rightarrow \frac{63}{100}\\[1em] \Rightarrow 0.63\end{aligned}$$

Hence, 5% of 12.6 = 0.63.

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

⇒ 20% of $\frac{1}{3}$

$$\begin{aligned}\Rightarrow \frac{20}{100} \times \frac{1}{3}\\[1em] \Rightarrow \frac{20}{300}\\[1em] \Rightarrow \frac{1}{15}\end{aligned}$$

Hence, 20% of $\mathbf{\frac{1}{3}}$ = $\mathbf{\frac{1}{15}}$.

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

⇒ 14% of ₹ 75

$$\begin{aligned}\Rightarrow \frac{14}{100} \times 75\\[1em] \Rightarrow \frac{1050}{100}\\[1em] \Rightarrow ₹\ 10.50\end{aligned}$$

Hence, 14% of ₹ 75 = ₹ 10.50.

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

⇒ 60% of 50 kg

$$\begin{aligned}\Rightarrow \frac{60}{100} \times 50\\[1em] \Rightarrow \frac{3000}{100}\\[1em] \Rightarrow 30 \text{ kg}\end{aligned}$$

Hence, 60% of 50 kg = 30 kg.

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

⇒ 8% of 65 cm

$$\begin{aligned}\Rightarrow \frac{8}{100} \times 65\\[1em] \Rightarrow \frac{520}{100}\\[1em] \Rightarrow 5.2 \text{ cm}\end{aligned}$$

Hence, 8% of 65 cm = 5.2 cm.

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

We know, 1 kg = 1000 g, so 3 kg = 3000 g.

⇒ 5% of 3000 g

$$\begin{aligned}\Rightarrow \frac{5}{100} \times 3000\\[1em] \Rightarrow \frac{15000}{100}\\[1em] \Rightarrow 150 \text{ g}\end{aligned}$$

Hence, 5% of 3 kg = 150 g.

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

We know, 1 litre = 1000 ml.

⇒ 10% of 1000 ml

$$\begin{aligned}\Rightarrow \frac{10}{100} \times 1000\\[1em] \Rightarrow \frac{10000}{100}\\[1em] \Rightarrow 100 \text{ ml}\end{aligned}$$

Hence, 10% of 1 litre = 100 ml.

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

We know, 1 year = 365 days.

⇒ 40% of 365 days

$$\begin{aligned}\Rightarrow \frac{40}{100} \times 365\\[1em] \Rightarrow \frac{14600}{100}\\[1em] \Rightarrow 146 \text{ days}\end{aligned}$$

Hence, 40% of 1 year = 146 days.

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

We know, 1 m = 100 cm.

⇒ 9% of 100 cm

$$\begin{aligned}\Rightarrow \frac{9}{100} \times 100\\[1em] \Rightarrow 9 \text{ cm}\end{aligned}$$

Hence, 9% of 1 m = 9 cm.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{19}{95} \times 100\right)$%

= $\frac{1900}{95}$%

= 20%

Hence, 19 is 20% of 95.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{32}{40} \times 100\right)$%

= $\frac{3200}{40}$%

= 80%

Hence, 32 is 80% of 40.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{117}{65} \times 100\right)$%

= $\frac{11700}{65}$%

= 180%

Hence, 117 is 180% of 65.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{29.4}{42} \times 100\right)$%

= $\frac{2940}{42}$%

= 70%

Hence, 29.4 is 70% of 42.

While comparing two quantities, they must be of the same kind and in the same units.

We know, ₹ 1 = 100 paise.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{43}{100} \times 100\right)$%

= 43%

Hence, 43 p is 43% of ₹ 1.

While comparing two quantities, they must be of the same kind and in the same units.

We know, 1 cm = 10 mm.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{16}{10} \times 100\right)$%

= $\frac{1600}{10}$%

= 160%

Hence, 16 mm is 160% of 1 cm.

While comparing two quantities, they must be of the same kind and in the same units.

We know, 1 m = 100 cm.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{8}{100} \times 100\right)$%

= 8%

Hence, 8 cm is 8% of 1 m.

While comparing two quantities, they must be of the same kind and in the same units.

We know, 1 km = 1000 m.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{635}{1000} \times 100\right)$%

= $\frac{63500}{1000}$%

= 63.5%

Hence, 635 m is 63.5% of 1 km.

While comparing two quantities, they must be of the same kind and in the same units.

We know, ₹ 1 = 100 paise, so ₹ 1.80 = (1.80 × 100) paise = 180 paise.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{27}{180} \times 100\right)$%

= $\frac{2700}{180}$%

= 15%

Hence, 27 p is 15% of ₹ 1.80.

While comparing two quantities, they must be of the same kind and in the same units.

We know, 1 m = 100 cm, so 1.5 m = (1.5 × 100) cm = 150 cm.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{48}{150} \times 100\right)$%

= $\frac{4800}{150}$%

= 32%

Hence, 48 cm is 32% of 1.5 m.

While comparing two quantities, they must be of the same kind and in the same units.

We know, 1 kg = 1000 gm, so 2.5 kg = (2.5 × 1000) gm = 2500 gm.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{175}{2500} \times 100\right)$%

= $\frac{17500}{2500}$%

= 7%

Hence, 175 gm is 7% of 2.5 kg.

While comparing two quantities, they must be of the same kind and in the same units.

2 minutes 24 seconds = (2 × 60 + 24) seconds = (120 + 24) seconds = 144 seconds.

1 hour = (60 × 60) seconds = 3600 seconds.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{144}{3600} \times 100\right)$%

= $\frac{14400}{3600}$%

= 4%

Hence, 2 minutes 24 seconds is 4% of 1 hour.

While comparing two quantities, they must be of the same kind and in the same units.

We know, 1 km = 1000 m, so 1.05 km = (1.05 × 1000) m = 1050 m.

Required percentage = $\left(\frac{\text{1st quantity}}{\text{2nd quantity}} \times 100\right)$%

= $\left(\frac{189}{1050} \times 100\right)$%

= $\frac{18900}{1050}$%

= 18%

Hence, 189 m is 18% of 1.05 km.

Let the required number be x.

8% of x = 18

$$\begin{aligned}\Rightarrow \frac{8}{100} \times x = 18\\[1em] \Rightarrow x = \frac{18 \times 100}{8}\\[1em] \Rightarrow x = \frac{1800}{8}\\[1em] \Rightarrow x = 225\end{aligned}$$

Hence, the required number is 225.

Let the required number be x.

6% of x = 8.1

$$\begin{aligned}\Rightarrow \frac{6}{100} \times x = 8.1\\[1em] \Rightarrow x = \frac{8.1 \times 100}{6}\\[1em] \Rightarrow x = \frac{810}{6}\\[1em] \Rightarrow x = 135\end{aligned}$$

Hence, the required number is 135.

Let the required amount be ₹ x.

12% of x = 21

$$\begin{aligned}\Rightarrow \frac{12}{100} \times x = 21\\[1em] \Rightarrow x = \frac{21 \times 100}{12}\\[1em] \Rightarrow x = \frac{2100}{12}\\[1em] \Rightarrow x = 175\end{aligned}$$

Hence, the required amount is ₹ 175.

Let the required length be x cm.

16% of x = 36

$$\begin{aligned}\Rightarrow \frac{16}{100} \times x = 36\\[1em] \Rightarrow x = \frac{36 \times 100}{16}\\[1em] \Rightarrow x = \frac{3600}{16}\\[1em] \Rightarrow x = 225\end{aligned}$$

Hence, the required length is 225 cm, i.e., 2.25 m.

Let the required number be x.

12.5% of x = 3.5

$$\begin{aligned}\Rightarrow \frac{12.5}{100} \times x = 3.5\\[1em] \Rightarrow x = \frac{3.5 \times 100}{12.5}\\[1em] \Rightarrow x = \frac{350}{12.5}\\[1em] \Rightarrow x = 28\end{aligned}$$

Hence, the required number is 28.

Maximum marks = 80.

Marks obtained by Kamal = 65% of 80

$$\begin{aligned}= \frac{65}{100} \times 80\\[1em] = \frac{5200}{100}\\[1em] = 52\end{aligned}$$

Hence, Kamal got 52 marks.

Marks obtained by Renu = 480 and maximum marks = 750.

Percentage of marks obtained = $\left(\frac{480}{750} \times 100\right)$%

$= \frac{48000}{750}$%

= 64%

Hence, Renu got 64% marks.

Percentage of marks in English = $\left(\frac{39}{60} \times 100\right)$%

$= \frac{3900}{60}$%

= 65%

Percentage of marks in Hindi = $\left(\frac{51}{75} \times 100\right)$%

$= \frac{5100}{75}$%

= 68%

Since 68% > 65%, her performance in Hindi was better than in English.

Hence, Geeta's performance was better in Hindi.

Total number of students = 640.

Number of students who passed = 544.

Number of students who failed = 640 − 544 = 96.

Percentage of students who failed = $\left(\frac{96}{640} \times 100\right)$%

$= \frac{9600}{640}$%

= 15%

Hence, 15% of the students failed.

Total number of students = 1360.

Percentage of students who passed = 85%.

Percentage of students who failed = (100 − 85)% = 15%.

Number of students who failed = 15% of 1360

$$\begin{aligned}= \frac{15}{100} \times 1360\\[1em] = \frac{20400}{100}\\[1em] = 204\end{aligned}$$

Hence, 204 students failed.

Marks obtained by Rahul = 247.

Since Rahul fails by 5 marks,

Pass marks = 247 + 5 = 252.

∴ 48% of maximum marks = 252

$$\begin{aligned}\Rightarrow \frac{48}{100} \times \text{(maximum marks)} = 252\\[1em] \Rightarrow \text{Maximum marks} = \frac{252 \times 100}{48}\\[1em] \Rightarrow \text{Maximum marks} = \frac{25200}{48}\\[1em] \Rightarrow \text{Maximum marks} = 525\end{aligned}$$

Hence, the maximum marks are 525.

Percentage of students present = 96%.

Percentage of absentees = (100 − 96)% = 4%.

∴ 4% of total strength = 82

$$\begin{aligned}\Rightarrow \frac{4}{100} \times \text{(total strength)} = 82\\[1em] \Rightarrow \text{Total strength} = \frac{82 \times 100}{4}\\[1em] \Rightarrow \text{Total strength} = \frac{8200}{4}\\[1em] \Rightarrow \text{Total strength} = 2050\end{aligned}$$

Hence, the total strength of the school is 2050.

Last year's population = 20320.

Increase in population = 5% of 20320

$$\begin{aligned}= \frac{5}{100} \times 20320\\[1em] = \frac{101600}{100}\\[1em] = 1016\end{aligned}$$

Present population = (last year's population + increase)

= 20320 + 1016

= 21336

Hence, the present population of the town is 21336.

Original price of the bat = ₹ 650.

Increase in its price = 6% of ₹ 650

$$\begin{aligned}= \frac{6}{100} \times 650\\[1em] = \frac{3900}{100}\\[1em] = ₹\ 39\end{aligned}$$

Increased price = (original price + increase)

= ₹ (650 + 39)

= ₹ 689

Hence, the increased price of the bat is ₹ 689.

Original price of the cooler = ₹ 7250.

Reduction in price = 12% of ₹ 7250

$$\begin{aligned}= \frac{12}{100} \times 7250\\[1em] = \frac{87000}{100}\\[1em] = ₹\ 870\end{aligned}$$

Reduced price = (original price − reduction)

= ₹ (7250 − 870)

= ₹ 6380

Hence, the reduced price of the cooler is ₹ 6380.

Value of the new car = ₹ 225000.

Depreciation in one year = 10% of ₹ 225000

$$\begin{aligned}= \frac{10}{100} \times 225000\\[1em] = \frac{2250000}{100}\\[1em] = ₹\ 22500\end{aligned}$$

Value after one year = (original value − depreciation)

= ₹ (225000 − 22500)

= ₹ 202500

Hence, the value of the car after one year will be ₹ 202500.

Height of Ashish = 175 cm.

Annu is 8% shorter than Ashish.

Difference in height = 8% of 175 cm

$$\begin{aligned}= \frac{8}{100} \times 175\\[1em] = \frac{1400}{100}\\[1em] = 14 \text{ cm}\end{aligned}$$

Annu's height = (175 − 14) cm = 161 cm

Hence, Annu's height is 161 cm.

Percentage of copper in the alloy = 60%.

Percentage of zinc in the alloy = (100 − 60)% = 40%.

Quantity of copper in 425 g of alloy = 60% of 425 g

$$\begin{aligned}= \frac{60}{100} \times 425\\[1em] = \frac{25500}{100}\\[1em] = 255 \text{ g}\end{aligned}$$

Quantity of zinc in 425 g of alloy = 40% of 425 g

$$\begin{aligned}= \frac{40}{100} \times 425\\[1em] = \frac{17000}{100}\\[1em] = 170 \text{ g}\end{aligned}$$

Hence, 425 g of the alloy contains 255 g of copper and 170 g of zinc.

Total oil in the tin = 25 litres.

Oil lost due to leakage = 2 litres.

Oil left in the tin = (25 − 2) litres = 23 litres.

Percentage of oil still there in the tin = $\left(\frac{23}{25} \times 100\right)$%

$= \frac{2300}{25}$%

= 92%

Hence, 92% of the oil is still there in the tin.

Total number of voters = 25000.

Number of votes polled = 80% of 25000

$$\begin{aligned}= \frac{80}{100} \times 25000\\[1em] = \frac{2000000}{100}\\[1em] = 20000\end{aligned}$$

Votes got by A = 60% of the total votes polled = 60% of 20000

$$\begin{aligned}= \frac{60}{100} \times 20000\\[1em] = \frac{1200000}{100}\\[1em] = 12000\end{aligned}$$

Votes got by B = (votes polled − votes got by A)

= 20000 − 12000

= 8000

Hence, B got 8000 votes.

Total money with Mr Mehta = ₹ 60000.

Percentage of money given to daughter, son and wife = (20 + 35 + 30)% = 85%.

Percentage of money donated = (100 − 85)% = 15%.

Money donated = 15% of ₹ 60000

$$\begin{aligned}= \frac{15}{100} \times 60000\\[1em] = \frac{900000}{100}\\[1em] = ₹\ 9000\end{aligned}$$

Hence, Mr Mehta donated ₹ 9000 to the Charitable Trust.

Required percentage = $\left(\frac{36}{850} \times 100\right)$%

$= \frac{3600}{850}$%

$= \frac{72}{17}$%

$= 4\frac{4}{17}$%

Hence, option 3 is the correct option.

Required percentage = $\left(\frac{78}{65} \times 100\right)$%

$= \frac{7800}{65}$%

= 120%

Hence, option 3 is the correct option.

15% of x = 9

$$\begin{aligned}\Rightarrow \frac{15}{100} \times x = 9\\[1em] \Rightarrow x = \frac{9 \times 100}{15}\\[1em] \Rightarrow x = \frac{900}{15}\\[1em] \Rightarrow x = 60\end{aligned}$$

Hence, option 4 is the correct option.

⇒ $6\frac{2}{3}$% = $\frac{20}{3}$%

$$\begin{aligned}\Rightarrow \frac{20}{3} \times \frac{1}{100}\\[1em] \Rightarrow \frac{20}{300}\\[1em] \Rightarrow \frac{1}{15}\\[1em] \Rightarrow 1 : 15\end{aligned}$$

Hence, option 3 is the correct option.

⇒ $16\frac{2}{3}$% = $\frac{50}{3}$%

$$\begin{aligned}\Rightarrow \frac{50}{3} \times \frac{1}{100}\\[1em] \Rightarrow \frac{50}{300}\\[1em] \Rightarrow \frac{1}{6}\end{aligned}$$

Hence, option 2 is the correct option.

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

⇒ 6.5

⇒ (6.5 × 100)%

⇒ 650%

Hence, option 2 is the correct option.

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

$\Rightarrow \frac{3}{5}$

$\Rightarrow \left(\frac{3}{5} \times 100\right)$%

$\Rightarrow \frac{300}{5}$%

$\Rightarrow 60$%

Hence, option 1 is the correct option.

We know, ₹ 1 = 100 paise, so ₹ 1.80 = (1.80 × 100) paise = 180 paise.

Required percentage = $\left(\frac{27}{180} \times 100\right)$%

$= \frac{2700}{180}$%

= 15%

Hence, option 2 is the correct option.

We know, 1 m = 100 cm, so 1.5 m = (1.5 × 100) cm = 150 cm.

Required percentage = $\left(\frac{48}{150} \times 100\right)$%

$= \frac{4800}{150}$%

= 32%

Hence, option 1 is the correct option.

We know, 1 kg = 1000 g, so 2.5 kg = (2.5 × 1000) g = 2500 g.

Required percentage = $\left(\frac{175}{2500} \times 100\right)$%

$= \frac{17500}{2500}$%

= 7%

Hence, option 3 is the correct option.

Original price = ₹ 4000 and reduced price = ₹ 3500.

Decrease in price = ₹ (4000 − 3500) = ₹ 500.

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

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

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

= 12.5%

Hence, option 3 is the correct option.

Let the total number of teachers be x.

Percentage of female teachers = 80%.

Percentage of male teachers = (100 − 80)% = 20%.

Then, 20% of x = 25

$$\begin{aligned}\Rightarrow \frac{20}{100} \times x = 25\\[1em] \Rightarrow x = \frac{25 \times 100}{20}\\[1em] \Rightarrow x = 125\end{aligned}$$

Number of female teachers = 80% of 125

$$\begin{aligned}= \frac{80}{100} \times 125\\[1em] = \frac{10000}{100}\\[1em] = 100\end{aligned}$$

Hence, option 2 is the correct option.

Total parts in the mixture = 8 + 2 = 10.

Out of 10 parts, milk = 8 parts.

Percentage of milk in the mixture = $\left(\frac{8}{10} \times 100\right)$%

$= \frac{800}{10}$%

= 80%

Hence, option 4 is the correct option.

Percentage of zinc and copper = (35 + 20)% = 55%.

Percentage of nickel = (100 − 55)% = 45%.

We know, 1 kg = 1000 g, so 1.5 kg = 1500 g.

Quantity of nickel in 1.5 kg of alloy = 45% of 1500 g

$$\begin{aligned}= \frac{45}{100} \times 1500\\[1em] = \frac{67500}{100}\\[1em] = 675 \text{ g}\end{aligned}$$

Hence, option 3 is the correct option.

(i) Let 25% of x = 45.

$$\begin{aligned}\Rightarrow \frac{25}{100} \times x = 45\\[1em] \Rightarrow x = \frac{45 \times 100}{25}\\[1em] \Rightarrow x = 180\end{aligned}$$

Hence, 25% of 180 = 45.

(ii) Let 15% of ₹ x = ₹ 9.

$$\begin{aligned}\Rightarrow \frac{15}{100} \times x = 9\\[1em] \Rightarrow x = \frac{9 \times 100}{15}\\[1em] \Rightarrow x = 60\end{aligned}$$

Hence, 15% of ₹ 60 = ₹ 9.

(iii) Let 8% of x kg = 480 g.

We know, 480 g = $\frac{480}{1000}$ kg = 0.48 kg.

$$\begin{aligned}\Rightarrow \frac{8}{100} \times x = 0.48\\[1em] \Rightarrow x = \frac{0.48 \times 100}{8}\\[1em] \Rightarrow x = 6\end{aligned}$$

Hence, 8% of 6 kg = 480 g.

(iv) Let 2% of x km = 100 m.

We know, 100 m = $\frac{100}{1000}$ km = 0.1 km.

$$\begin{aligned}\Rightarrow \frac{2}{100} \times x = 0.1\\[1em] \Rightarrow x = \frac{0.1 \times 100}{2}\\[1em] \Rightarrow x = 5\end{aligned}$$

Hence, 2% of 5 km = 100 m.

(v) Let 9% of x m = 18 cm.

We know, 18 cm = $\frac{18}{100}$ m = 0.18 m.

$$\begin{aligned}\Rightarrow \frac{9}{100} \times x = 0.18\\[1em] \Rightarrow x = \frac{0.18 \times 100}{9}\\[1em] \Rightarrow x = 2\end{aligned}$$

Hence, 9% of 2 m = 18 cm.

(i) We know, 2.5 kg = 2500 g.

Required percentage = $\left(\frac{175}{2500} \times 100\right)$%

= $\frac{17500}{2500}$%

= 7%

Hence, 175 g is 7% of 2.5 kg.

(ii) To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\frac{3}{5} = \left(\frac{3}{5} \times 100\right)$%

= $\frac{300}{5}$%

= 60%

Hence, $\mathbf{\frac{3}{5}}$ expressed as percentage is 60%.

(iii) 6% of x = 0.21

$$\begin{aligned}\Rightarrow \frac{6}{100} \times x = 0.21\\[1em] \Rightarrow x = \frac{0.21 \times 100}{6}\\[1em] \Rightarrow x = \frac{21}{6}\\[1em] \Rightarrow x = 3.5\end{aligned}$$

Hence, if 6% of x is 0.21, then x = 3.5.

(iv) Percentage of marks = $\left(\frac{57}{150} \times 100\right)$%

= $\frac{5700}{150}$%

= 38%

Hence, Renu got 38% marks.

(v) Increase = 15% of ₹ 80

= $\frac{15}{100} \times 80$

= ₹ 12.

Increased amount = ₹ (80 + 12) = ₹ 92.

Hence, when ₹ 80 is increased by 15%, we get ₹ 92.

(vi) Decrease = 15% of ₹ 120

= $\frac{15}{100} \times 120$

= ₹ 18.

Decreased amount = ₹ (120 − 18) = ₹ 102.

Hence, ₹ 120 decreased by 15% = ₹ 102.

(i) 0.023 = (0.023 × 100)% = 2.3%.

Hence, the statement is true (T).

(ii) By definition, per cent means per hundred or out of 100.

Hence, the statement is true (T).

(iii) We know that,

1 cm = 10 mm

5% of 1 cm = $\frac{5}{100} \times 10$ mm = 0.5 mm ≠ 5 mm.

Hence, the statement is false (F).

(iv) 123% = $\frac{123}{100}$ = 1.23 ≠ 12.3.

Hence, the statement is false (F).

(v) 8% = $\frac{8}{100}$ = 0.08 ≠ 0.8.

Hence, the statement is false (F).

1. Let the total number of students be x.

45% of x = 36

$$\begin{aligned}\Rightarrow \frac{45}{100} \times x = 36\\[1em] \Rightarrow x = \frac{36 \times 100}{45}\\[1em] \Rightarrow x = \frac{3600}{45}\\[1em] \Rightarrow x = 80\end{aligned}$$

Hence, option (b) is the correct option.

2. Total number of students = 80.

Number of students who preferred going to the zoo = 15% of 80.

$$\begin{aligned}= \frac{15}{100} \times 80\\[1em] = \frac{1200}{100}\\[1em] = 12\end{aligned}$$

Hence, option (c) is the correct option.

3. Total number of students = 80.

Number of students who preferred going to the museum = 10% of 80

$$\begin{aligned}= \frac{10}{100} \times 80\\[1em] = \frac{800}{100}\\[1em] = 8\end{aligned}$$

Hence, option (a) is the correct option.

4. Percentage of students with no preference = [100 − (45 + 15 + 10)]% = (100 − 70)% = 30%.

Percentage of students who wanted to go to the amusement park = 45%.

Required ratio = 30% : 45%

$= \frac{30}{45}$

$= \frac{2}{3}$

= 2 : 3

Hence, option (c) is the correct option.

1. Percentage of marks in English = $\left(\frac{54}{75} \times 100\right)$%

$= \frac{5400}{75}$%

= 72%

Hence, option (a) is the correct option.

2. Percentage of marks in Science = $\left(\frac{60}{80} \times 100\right)$%

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

= 75%

Hence, option (c) is the correct option.

3. Percentage of marks in English = $\left(\frac{54}{75} \times 100\right)$% = 72%

Percentage of marks in Hindi = $\left(\frac{51}{75} \times 100\right)$% = 68%

Percentage of marks in Mathematics = $\left(\frac{64}{80} \times 100\right)$% = 80%

Percentage of marks in Science = $\left(\frac{60}{80} \times 100\right)$% = 75%

Since 80% is the highest percentage, Rohan performed the best in Mathematics.

Hence, option (d) is the correct option.

4. Percentage of marks in English = 72%, Hindi = 68%, Mathematics = 80% and Science = 75%.

Since 68% is the lowest percentage, Rohan performed the worst in Hindi.

Hence, option (b) is the correct option.

An improper fraction is always greater than 1. On multiplying it by 100, the result is always greater than 100.

For example, $\frac{5}{4} = \left(\frac{5}{4} \times 100\right)$% = 125% > 100%.

So, Assertion (A) is true.

We know that % means per hundred, so in any question the % sign can be replaced with $\frac{1}{100}$. So, Reason (R) is true.

However, the Assertion follows from the fact that a fraction or decimal is converted into a percentage by multiplying it by 100, and not from replacing the % sign with $\frac{1}{100}$. So, Reason (R) is not the correct explanation of Assertion (A).

Hence, option 2 is the correct option.

Total number of students = 600.

Number of students who went for the picnic = 150.

Number of students who did not go for the picnic = 600 − 150 = 450.

Percentage of students who did not go for the picnic = $\left(\frac{450}{600} \times 100\right)$%

$= \frac{45000}{600}$%

= 75%

So, Assertion (A) is true.

To find the percentage of a given quantity, we convert the given percentage into a fraction and multiply it by the given quantity, and not divide it by the given quantity. So, Reason (R) is false.

Assertion (A) is true and Reason (R) is false.

Hence, option 3 is the correct option.

Original price = ₹ 89.50 and new price = ₹ 99.45.

Increase in price = ₹ (99.45 − 89.50) = ₹ 9.95.

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

$= \left(\frac{9.95}{89.50} \times 100\right)$%

$= \frac{995}{89.5}$%

= 11.12% (to 2 decimal places)

Hence, option 3 is the correct option.

Percentage of students who like Math and Science combined = (40 + 30)% = 70%.

Number of students who like Math and Science combined = 70% of 300

$$\begin{aligned}= \frac{70}{100} \times 300\\[1em] = \frac{21000}{100}\\[1em] = 210\end{aligned}$$

Hence, option 3 is the correct option.

Let the two numbers be 3x and 5x. Then, the smaller number = 3x and the larger number = 5x.

40% of the smaller number = 24

$$\begin{aligned}\Rightarrow \frac{40}{100} \times 3x = 24\\[1em] \Rightarrow \frac{120x}{100} = 24\\[1em] \Rightarrow x = \frac{24 \times 100}{120}\\[1em] \Rightarrow x = 20\end{aligned}$$

So, the larger number = 5x = 5 × 20 = 100.

60% of the larger number = 60% of 100

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

= 60

Hence, option 4 is the correct option.

Percentage of the garden used for vegetables and flowers = (25 + 30)% = 55%.

Area used for vegetables and flowers = 55% of 800 m²

$$\begin{aligned}= \frac{55}{100} \times 800\\[1em] = \frac{44000}{100}\\[1em] = 440 \text{ m}^2\end{aligned}$$

Hence, option 1 is the correct option.

Percentage of harvest used for personal consumption and sold to the market = (20 + 40)% = 60%.

Percentage of harvest stored = (100 − 60)% = 40%.

Let the total harvest be x tonnes.

40% of x = 60

$$\begin{aligned}\Rightarrow \frac{40}{100} \times x = 60\\[1em] \Rightarrow x = \frac{60 \times 100}{40}\\[1em] \Rightarrow x = 150\end{aligned}$$

Hence, option 3 is the correct option.

Let the required number be x.

75% of x + 75 = x

$$\begin{aligned}\Rightarrow \frac{75}{100} \times x + 75 = x\\[1em] \Rightarrow \frac{3x}{4} + 75 = x\\[1em] \Rightarrow x - \frac{3x}{4} = 75\\[1em] \Rightarrow \frac{x}{4} = 75\\[1em] \Rightarrow x = 75 \times 4\\[1em] \Rightarrow x = 300\end{aligned}$$

Hence, option 3 is the correct option.

The test was out of 50 marks.

Average score of the three friends = 82% of 50

$$\begin{aligned}= \frac{82}{100} \times 50\\[1em] = \frac{4100}{100}\\[1em] = 41 \text{ marks}\end{aligned}$$

Total marks of the three friends = 41 × 3 = 123.

Marks of Ajay and Kapil = 40 + 36 = 76.

Marks scored by Varun = 123 − 76 = 47.

Hence, option 3 is the correct option.

Since equal quantities of A and B are mixed to prepare 10 kg of mixture,

Quantity of alloy A = quantity of alloy B = 5 kg.

In alloy A, gold : copper = 3 : 2, so sum of ratio terms = 3 + 2 = 5.

Gold in 5 kg of alloy A = $\frac{3}{5} \times 5$ = 3 kg.

In alloy B, gold : copper = 4 : 3, so sum of ratio terms = 4 + 3 = 7.

Gold in 5 kg of alloy B = $\frac{4}{7} \times 5 = \frac{20}{7}$ kg.

Total gold in the mixture = $3 + \frac{20}{7} = \frac{21 + 20}{7} = \frac{41}{7}$ kg.

Percentage of gold in the final mixture = $\left(\frac{41}{7 \times 10} \times 100\right)$%

$= \frac{4100}{70}$%

$= \frac{410}{7}$%

= 58.57% (approx.)

Hence, option 2 is the correct option.