Percentage — Exercise 6(A)

Convert the following into a fraction:

68%

Answer

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

$\Rightarrow 68 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{68}{100}\\[1em] \Rightarrow \dfrac{17}{25}$

Hence, 68% = $\mathbf{\dfrac{17}{25}}$.

Convert the following into a fraction:

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

Answer

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

$3\dfrac{1}{3}$% = $\dfrac{10}{3}$%

$\Rightarrow \dfrac{10}{3} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{10}{300}\\[1em] \Rightarrow \dfrac{1}{30}$

Hence, $\mathbf{3\dfrac{1}{3}}$% = $\mathbf{\dfrac{1}{30}}$.

Convert the following into a fraction:

224%

Answer

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

$\Rightarrow 224 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{224}{100}\\[1em] \Rightarrow \dfrac{56}{25}\\[1em] \Rightarrow 2\dfrac{6}{25}$

Hence, 224% = $\mathbf{2\dfrac{6}{25}}$.

Convert the following into a fraction:

0.05%

Answer

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

$\Rightarrow 0.05 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{0.05}{100}\\[1em] \Rightarrow \dfrac{5}{10000}\\[1em] \Rightarrow \dfrac{1}{2000}$

Hence, 0.05% = $\mathbf{\dfrac{1}{2000}}$.

Convert the following into a percentage:

$\dfrac{2}{15}$

Answer

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

$\Rightarrow \dfrac{2}{15} \times 100$%

$\Rightarrow \dfrac{200}{15}$%

$\Rightarrow \dfrac{40}{3}$%

$\Rightarrow 13\dfrac{1}{3}$%

Hence, $\mathbf{\dfrac{2}{15}} = \mathbf{13\dfrac{1}{3}}$%.

Convert the following into a percentage:

$\dfrac{9}{40}$

Answer

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

$\Rightarrow \dfrac{9}{40} \times 100$%

$\Rightarrow \dfrac{900}{40}$%

$\Rightarrow \dfrac{45}{2}$%

$\Rightarrow 22\dfrac{1}{2}$%

Hence, $\mathbf{\dfrac{9}{40}} = \mathbf{22\dfrac{1}{2}}$%.

Convert the following into a percentage:

$1\dfrac{2}{3}$

Answer

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

$1\dfrac{2}{3}$ = $\dfrac{5}{3}$

$\Rightarrow \dfrac{5}{3} \times 100$%

$\Rightarrow \dfrac{500}{3}$%

$\Rightarrow 166\dfrac{2}{3}$%

Hence, $\mathbf{1\dfrac{2}{3}} = \mathbf{166\dfrac{2}{3}}$%.

Convert the following into a percentage:

$2\dfrac{2}{5}$

Answer

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

$2\dfrac{2}{5} = \dfrac{12}{5}$

$\Rightarrow \dfrac{12}{5} \times 100$%

$\Rightarrow \dfrac{1200}{5}$%

⇒ 240%

Hence, $\mathbf{2\dfrac{2}{5}}$ = 240%.

Express the following ratio as a percentage:

13 : 20

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

⇒ 13 : 20

$\Rightarrow \dfrac{13}{20}$

$\Rightarrow \dfrac{13}{20} \times 100$%

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

⇒ 65%

Hence, 13 : 20 = 65%.

Express the following ratio as a percentage:

11 : 18

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

⇒ 11 : 18

$\Rightarrow \dfrac{11}{18}$

$\Rightarrow \dfrac{11}{18} \times 100$%

$\Rightarrow \dfrac{1100}{18}$%

$\Rightarrow \dfrac{550}{9}$%

$\Rightarrow 61\dfrac{1}{9}$%

Hence, 11 : 18 = $\mathbf{61\dfrac{1}{9}}$%.

Express the following ratio as a percentage:

87 : 25

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

⇒ 87 : 25

$\Rightarrow \dfrac{87}{25}$

$\Rightarrow \dfrac{87}{25} \times 100$%

$\Rightarrow \dfrac{8700}{25}$%

⇒ 348%

Hence, 87 : 25 = 348%.

Express the following ratio as a percentage:

$6\dfrac{1}{4} : 4\dfrac{3}{8}$

Answer

To convert a ratio into a percentage, first convert the given ratio into a fraction and then convert the fraction into a percentage.

$6\dfrac{1}{4} : 4\dfrac{3}{8} = \dfrac{25}{4} : \dfrac{35}{8}$

$\Rightarrow \dfrac{\dfrac{25}{4}}{\dfrac{35}{8}}\\[1em] \Rightarrow \dfrac{25}{4} \times \dfrac{8}{35}\\[1em] \Rightarrow \dfrac{200}{140}\\[1em] \Rightarrow \dfrac{10}{7}$

Converting the ratio into percentage:

$\Rightarrow \dfrac{10}{7} \times 100$%

$\Rightarrow \dfrac{1000}{7}$%

$\Rightarrow 142\dfrac{6}{7}$%

Hence, $\mathbf{6\dfrac{1}{4} : 4\dfrac{3}{8} = 142\dfrac{6}{7}}$%.

Express the following decimal as a percentage:

0.2

Answer

To convert a decimal into a percentage, first convert the given decimal into a fraction and then multiply the fraction by 100 and put the % sign.

0.2 = $\dfrac{2}{10}$

$\Rightarrow \dfrac{2}{10} \times 100$%

$\Rightarrow \dfrac{200}{10}$%

⇒ 20%

Hence, 0.2 = 20%.

Express the following decimal as a percentage:

0.06

Answer

To convert a decimal into a percentage, first convert the given decimal into a fraction and then multiply the fraction by 100 and put the % sign.

0.06 = $\dfrac{6}{100}$

$\Rightarrow \dfrac{6}{100} \times 100$%

$\Rightarrow \dfrac{600}{100}$%

⇒ 6%

Hence, 0.06 = 6%.

Express the following decimal as a percentage:

0.008

Answer

To convert a decimal into a percentage, first convert the given decimal into a fraction and then multiply the fraction by 100 and put the % sign.

0.008 = $\dfrac{8}{1000}$

$\Rightarrow \dfrac{8}{1000} \times 100$%

$\Rightarrow \dfrac{800}{1000}$%

⇒ 0.8%

Hence, 0.008 = 0.8%.

Express the following decimal as a percentage:

2.4

Answer

To convert a decimal into a percentage, first convert the given decimal into a fraction and then multiply the fraction by 100 and put the % sign.

2.4 = $\dfrac{24}{10}$

$\Rightarrow \dfrac{24}{10} \times 100$%

$\Rightarrow \dfrac{2400}{10}$%

⇒ 240%

Hence, 2.4 = 240%.

Express the following percentage as a decimal:

25%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$\Rightarrow \dfrac{25}{100}$

⇒ 0.25

Hence, 25% = 0.25.

Express the following percentage as a decimal:

4%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$\Rightarrow \dfrac{4}{100}$

⇒ 0.04

Hence, 4% = 0.04.

Express the following percentage as a decimal:

$3\dfrac{1}{5}$%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$3\dfrac{1}{5}$% = $\dfrac{16}{5}$%

$\Rightarrow \dfrac{16}{5} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{16}{500}\\[1em] \Rightarrow 0.032$

Hence, $\mathbf{3\dfrac{1}{5}}$% = 0.032.

Express the following percentage as a decimal:

0.3%

Answer

To convert a percentage into a decimal, first convert the percentage into a fraction by replacing the % sign with $\dfrac{1}{100}$, then convert the fraction into a decimal.

$\Rightarrow \dfrac{0.3}{100}\\[1em] \Rightarrow \dfrac{3}{1000}\\[1em] \Rightarrow 0.003$

Hence, 0.3% = 0.003.

Express the following as a ratio:

48%

Answer

To convert a percentage into a ratio, first convert the given percentage into a fraction in the simplest form and then express it as a ratio.

$\Rightarrow \dfrac{48}{100}\\[1em] \Rightarrow \dfrac{12}{25}\\[1em] \Rightarrow 12 : 25$

Hence, 48% = 12 : 25.

Express the following as a ratio:

$26\dfrac{2}{3}$%

Answer

To convert a percentage into a ratio, first convert the given percentage into a fraction in the simplest form and then express it as a ratio.

$26\dfrac{2}{3}$% = $\dfrac{80}{3}$%

$\Rightarrow \dfrac{80}{3} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{80}{300}\\[1em] \Rightarrow \dfrac{4}{15}\\[1em] \Rightarrow 4 : 15$

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

Express the following as a ratio:

0.06%

Answer

To convert a percentage into a ratio, first convert the given percentage into a fraction in the simplest form and then express it as a ratio.

$\Rightarrow \dfrac{0.06}{100}\\[1em] \Rightarrow \dfrac{6}{10000}\\[1em] \Rightarrow \dfrac{3}{5000}\\[1em] \Rightarrow 3 : 5000$

Hence, 0.06% = 3 : 5000.

Express the following as a ratio:

120%

Answer

To convert a percentage into a ratio, first convert the given percentage into a fraction in the simplest form and then express it as a ratio.

$\Rightarrow \dfrac{120}{100}\\[1em] \Rightarrow \dfrac{6}{5}\\[1em] \Rightarrow 6 : 5$

Hence, 120% = 6 : 5.

Find the value of:

33% of ₹50

Answer

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

$\Rightarrow \dfrac{33}{100} \times 50\\[1em] \Rightarrow \dfrac{1650}{100}\\[1em] \Rightarrow ₹16.50$

Hence, 33% of ₹50 = ₹16.50.

Find the value of:

$6\dfrac{2}{3}$% of 3 m

Answer

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

3 m = (3 x 100) cm = 300 cm

$6\dfrac{2}{3}$% of 3 m = $\dfrac{20}{3}$% of 300 cm

$\Rightarrow \dfrac{20}{3} \times \dfrac{1}{100} \times 300\\[1em] \Rightarrow \dfrac{6000}{300}\\[1em] \Rightarrow 20 \text{ cm}$

Hence, $\mathbf{6\dfrac{2}{3}}$% of 3 m = 20 cm.

Find the value of:

0.6% of 35 kg

Answer

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

35 kg = (35 x 1000) g = 35000 g

$\Rightarrow \dfrac{0.6}{100} \times 35000\\[1em] \Rightarrow \dfrac{21000}{100}\\[1em] \Rightarrow 210 \text{ g}$

Hence, 0.6% of 35 kg = 210 g.

Find the value of:

$3\dfrac{1}{4}$% of 5 l

Answer

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

5 l = (5 x 1000) ml = 5000 ml

$3\dfrac{1}{4}$% of 5 l = $\dfrac{13}{4}$% of 5000 ml

$\Rightarrow \dfrac{13}{4} \times \dfrac{1}{100} \times 5000\\[1em] \Rightarrow \dfrac{65000}{400}\\[1em] \Rightarrow 162.5 \text{ ml}$

Hence, $\mathbf{3\dfrac{1}{4}}$% of 5 l = 162.5 ml.

What per cent of ₹9 is ₹5?

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

Required percentage = $\dfrac{5}{9} \times 100$%

= $\dfrac{500}{9}$%

= $55\dfrac{5}{9}$%

Hence, ₹5 is $\mathbf{55\dfrac{5}{9}}$% of ₹9.

What per cent of 32 m is 80 m?

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

Required percentage = $\dfrac{80}{32} \times 100$%

= $\dfrac{8000}{32}$%

= 250%

Hence, 80 m is 250% of 32 m.

What per cent of 50 kg is 65 kg?

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

Required percentage = $\dfrac{65}{50} \times 100$%

= $\dfrac{6500}{50}$%

= 130%

Hence, 65 kg is 130% of 50 kg.

What per cent of 5 litres is 400 ml?

Answer

To express $x$ as a percentage of $y$, percentage = $\Big(\dfrac{x}{y} \times 100\Big)$%. Both the quantities must be of the same kind (in the same units).

5 litres = (5 x 1000) ml = 5000 ml

Required percentage = $\dfrac{400}{5000} \times 100$%

= $\dfrac{40000}{5000}$%

= 8%

Hence, 400 ml is 8% of 5 litres.

If 8% of a number is 24, find the number.

Answer

Let the required number be $x$.

According to the given condition,

8% of $x$ = 24

$\Rightarrow \dfrac{8}{100} \times x = 24 \\[1em] \Rightarrow \dfrac{8x}{100} = 24 \\[1em] \Rightarrow x = \dfrac{24 \times 100}{8} \\[1em] \Rightarrow x = \dfrac{2400}{8} \\[1em] \Rightarrow x = 300$

Hence, the required number is 300.

If 7.25% of a number is 2.9, find the number.

Answer

Let the required number be $x$.

According to the given condition,

7.25% of $x$ = 2.9

$\Rightarrow \dfrac{7.25}{100} \times x = 2.9 \\[1em] \Rightarrow \dfrac{7.25x}{100} = 2.9 \\[1em] \Rightarrow x = \dfrac{2.9 \times 100}{7.25} \\[1em] \Rightarrow x = \dfrac{290}{7.25} \\[1em] \Rightarrow x = 40$

Hence, the required number is 40.

If $6\dfrac{2}{3}$% of a number is 1, find the number.

Answer

Let the required number be $x$.

$6\dfrac{2}{3}$% = $\dfrac{20}{3}$%

According to the given condition,

$\dfrac{20}{3}$% of $x$ = 1

$\Rightarrow \dfrac{20}{3} \times \dfrac{1}{100} \times x = 1 \\[1em] \Rightarrow \dfrac{20x}{300} = 1 \\[1em] \Rightarrow \dfrac{x}{15} = 1 \\[1em] \Rightarrow x = 15$

Hence, the required number is 15.

Increase 75 by 24%.

Answer

If a value $a$ is increased by $x$%, then new value = $\Big(1 + \dfrac{x}{100}\Big)a$.

On increasing 75 by 24%, we get

$\text{New number} = \Big(1 + \dfrac{24}{100}\Big) \times 75 \\[1em] = \dfrac{124}{100} \times 75 \\[1em] = \dfrac{31}{25} \times 75 \\[1em] = \dfrac{2325}{25} \\[1em] = 93$

Hence, on increasing 75 by 24% we get 93.

Decrease 375 by 8%.

Answer

If a value $a$ is decreased by $x$%, then new value = $\Big(1 - \dfrac{x}{100}\Big)a$.

On decreasing 375 by 8%, we get

$\text{New number} = \Big(1 - \dfrac{8}{100}\Big) \times 375 \\[1em] = \dfrac{92}{100} \times 375 \\[1em] = \dfrac{23}{25} \times 375 \\[1em] = \dfrac{8625}{25} \\[1em] = 345$

Hence, on decreasing 375 by 8% we get 345.

What number when increased by 15% becomes 276?

Answer

Let the required number be $x$.

Since the number is increased by 15%, we get

$x + \dfrac{x \times 15}{100} = 276 \\[1em] \Rightarrow \dfrac{100x + 15x}{100} = 276 \\[1em] \Rightarrow \dfrac{115x}{100} = 276 \\[1em] \Rightarrow x = \dfrac{276 \times 100}{115} \\[1em] \Rightarrow x = \dfrac{27600}{115} \\[1em] \Rightarrow x = 240$

Hence, the required number is 240.

What number when decreased by 8% becomes 345?

Answer

Let the required number be $x$.

Since the number is decreased by 8%, we get

$x - \dfrac{x \times 8}{100} = 345 \\[1em] \Rightarrow \dfrac{100x - 8x}{100} = 345 \\[1em] \Rightarrow \dfrac{92x}{100} = 345 \\[1em] \Rightarrow x = \dfrac{345 \times 100}{92} \\[1em] \Rightarrow x = \dfrac{34500}{92} \\[1em] \Rightarrow x = 375$

Hence, the required number is 375.