Percentage - Exercise 9(A)

Express each of the following as a per cent :

(i) $\dfrac{3}{5}$

(ii) $\dfrac{5}{16}$

(iii) $\dfrac{19}{40}$

(iv) $3\dfrac{1}{4}$

Answer

(i) $\dfrac{3}{5}$

= $\Big( \dfrac{3}{5} \times 100 \Big)$%

= $(3 \times 20)$%

= 60%

Hence, the answer is 60%

(ii) $\dfrac{5}{16}$

= $\Big( \dfrac{5}{16} \times 100 \Big)$%

= $\Big( \dfrac{5 \times 25}{4} \Big)$%

= $\dfrac{125}{4}$%

= 31.25%

Hence, the answer is 31.25%

(iii) $\dfrac{19}{40}$

= $\Big( \dfrac{19}{40} \times 100 \Big)$%

= $\Big( \dfrac{19 \times 5}{2} \Big)$%

= $\dfrac{95}{2}$%

= 47.5%

Hence, the answer is 47.5%

(iv) $3\dfrac{1}{4}$

First, convert the mixed fraction to an improper fraction:

$3\dfrac{1}{4} = \dfrac{13}{4}$

We have:

$\dfrac{13}{4} = \Big( \dfrac{13}{4} \times 100 \Big)$%

= $(13 \times 25)$%

= 325%

Hence, the answer is 325%

Express each of the following as a per cent :

(i) 0.45

(ii) 0.03

(iii) 0.1

(iv) 2.45

Answer

(i) 0.45

First, convert decimal into fraction:

0.45 = $\dfrac{45}{100}$

We have:

$\dfrac{45}{100} = \Big( \dfrac{45}{100} \times 100 \Big)$% = 45%

Hence, the answer is 45%

(ii) 0.03

First, convert decimal into fraction:

0.03 = $\dfrac{3}{100}$

We have:

$\dfrac{3}{100} = \Big( \dfrac{3}{100} \times 100 \Big)$% = 3%

Hence, the answer is 3%

(iii) 0.1

First, convert decimal into fraction:

0.1 = $\dfrac{1}{10}$

We have:

$\dfrac{1}{10} = \Big( \dfrac{1}{10} \times 100 \Big)$% = $(1 \times 10)$% = 10%

Hence, the answer is 10%

(iv) 2.45

We have:

2.45 = $\dfrac{245}{100}$

First, convert decimal into fraction:

$\dfrac{245}{100} = \Big( \dfrac{245}{100} \times 100 \Big)$% = 245%

Hence, the answer is 245%

Express each of the following as a per cent :

(i) 5 : 8

(ii) 11 : 18

(iii) 1 : 5

(iv) 5 : 4

Answer

(i) 5 : 8

First, convert ratio into fraction:

5 : 8 = $\dfrac{5}{8}$

We have:

$\dfrac{5}{8} = \Big( \dfrac{5}{8} \times 100 \Big)$%

= $\Big( \dfrac{5 \times 25}{2} \Big)$%

= $\dfrac{125}{2}$%

= 62.5%

Hence, the answer is 62.5%

(ii) 11 : 18

First, convert ratio into fraction:

11 : 18 = $\dfrac{11}{18}$

We have:

$\dfrac{11}{18} = \Big( \dfrac{11}{18} \times 100 \Big)$%

= $\Big( \dfrac{11 \times 50}{9} \Big)$%

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

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

Hence, the answer is $61\dfrac{1}{9}$%

(iii) 1 : 5

First, convert ratio into fraction:

1 : 5 = $\dfrac{1}{5}$

We have:

$\dfrac{1}{5} = \Big( \dfrac{1}{5} \times 100 \Big)$% = 20%

Hence, the answer is 20%

(iv) 5 : 4

First, convert ratio into fraction:

5 : 4 = $\dfrac{5}{4}$

We have:

$\dfrac{5}{4} = \Big( \dfrac{5}{4} \times 100 \Big)$% = (5 × 25)% = 125%

Hence, the answer is 125%

Express each of the following as a fraction :

(i) 24%

(ii) $12\dfrac{1}{2}$%

(iii) $6\dfrac{2}{3}$%

(iv) 165%

Answer

(i) 24%

To express a percentage as a fraction, divide the number by 100 and remove the % sign.

24% = $\dfrac{24}{100} = \dfrac{6}{25}$

Hence, the answer is $\dfrac{6}{25}$

(ii) $12\dfrac{1}{2}$%

First, convert the mixed fraction to an improper fraction:

$12\dfrac{1}{2} = \dfrac{25}{2}$

To express a percentage as a fraction, divide the number by 100 and remove the % sign.

$\dfrac{25}{2}$% = $\left( \dfrac{25}{2} \times \dfrac{1}{100} \right) = \dfrac{25}{200} = \dfrac{1}{8}$

Hence, the answer is $\dfrac{1}{8}$

(iii) $6\dfrac{2}{3}$%

First, convert the mixed fraction to an improper fraction:

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

To express a percentage as a fraction, divide the number by 100 and remove the % sign.

$\dfrac{20}{3}$% = $\left( \dfrac{20}{3} \times \dfrac{1}{100} \right) = \dfrac{20}{300} = \dfrac{1}{15}$

Hence, the answer is $\dfrac{1}{15}$

(iv) 165%

To express a percentage as a fraction, divide the number by 100 and remove the % sign.

165% = $\dfrac{165}{100} = \dfrac{33}{20} = 1\dfrac{13}{20}$

Hence, the answer is $1\dfrac{13}{20}$

Express each of the following as a fraction :

(i) 0.25%

(ii) 0.05%

(iii) 2.25%

(iv) 0.006%

Answer

(i) 0.25%

To express a percentage with a decimal as a fraction, divide the number by 100 and remove the % sign.

0.25% = $\dfrac{0.25}{100}$

Multiply numerator and denominator by 100 to remove the decimal:

$\dfrac{0.25}{100} = \dfrac{0.25 \times 100}{100 \times 100} \\[1em] = \dfrac{25}{10000} \\[1em] = \dfrac{1}{400}$

Hence, the answer is $\dfrac{1}{400}$

(ii) 0.05%

To express a percentage with a decimal as a fraction, divide the number by 100 and remove the % sign.

0.05% = $\dfrac{0.05}{100}$

Multiply numerator and denominator by 100 to remove the decimal:

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

Hence, the answer is $\dfrac{1}{2000}$

(iii) 2.25%

To express a percentage with a decimal as a fraction, divide the number by 100 and remove the % sign.

2.25% = $\dfrac{2.25}{100}$

Multiply numerator and denominator by 100 to remove the decimal:

$\dfrac{2.25}{100} = \dfrac{2.25 \times 100}{100 \times 100} \\[1em] = \dfrac{225}{10000} \\[1em] = \dfrac{9}{400}$

Hence, the answer is $\dfrac{9}{400}$

(iv) 0.006%

To express a percentage with a decimal as a fraction, divide the number by 100 and remove the % sign.

0.006% = $\dfrac{0.006}{100}$

Multiply numerator and denominator by 1000 to remove the decimal:

$\dfrac{0.006}{100} = \dfrac{0.006 \times 1000}{100 \times 1000} \\[1em] = \dfrac{6}{100000} \\[1em] = \dfrac{3}{50000}$

Hence, the answer is $\dfrac{3}{50000}$

Express each of the following as a ratio :

(i) 12%

(ii) $\dfrac{3}{5}$%

(iii) 7.5%

(iv) 0.36%

Answer

(i) 12%

To express a percentage as a ratio, we first write it as a fraction with a denominator of 100.

12% = $\dfrac{12}{100} = \dfrac{3}{25} = 3 : 25$

Hence, the answer is 3 : 25

(ii) $\dfrac{3}{5}$%

To express a percentage as a ratio, we first write it as a fraction with a denominator of 100.

$\dfrac{3}{5}$% = $\left( \dfrac{3}{5} \times \dfrac{1}{100} \right) = \dfrac{3}{500} = 3 : 500$

Hence, the answer is 3 : 500

(iii) 7.5%

To express a percentage as a ratio, we first write it as a fraction with a denominator of 100.

7.5% = $\dfrac{7.5}{100}$

Multiply numerator and denominator by 10 to remove the decimal:

$\dfrac{7.5}{100} =\dfrac{7.5 \times 10}{100 \times 10} = \dfrac{75}{1000} = \dfrac{3}{40} = 3 : 40$

Hence, the answer is 3 : 40

(iv) 0.36%

0.36% = $\dfrac{0.36}{100}$

Multiply numerator and denominator by 100 to remove the decimal:

$\dfrac{0.36}{100} = \dfrac{0.36 \times 100}{100 \times 100} = \dfrac{36}{10000} = \dfrac{9}{2500} = 9 : 2500$

Hence, the answer is 9 : 2500

Find:

(i) 25% of ₹ 7

(ii) $7\dfrac{1}{2}$% of ₹ 40

(iii) 1% of ₹ 325

(iv) 8% of 5 kg

(v) $16\dfrac{2}{3}$% of 9 m

(vi) 0.6% of 5 km

(vii) $6\dfrac{1}{4}$% of (1 hour 20 min.)

Answer

(i) We have:

25% of ₹ 7

$= ₹ \dfrac{25}{100} \times 7 \\[1em] = ₹ \dfrac{1}{4} \times 7 \\[1em] = ₹ \dfrac{7}{4} \\[1em] = ₹ 1.75$

Hence, the answer is ₹ 1.75

(ii) We have:

$7\dfrac{1}{2}$% of ₹ 40

First, convert to an improper fraction:

$7\dfrac{1}{2}$% = $\dfrac{15}{2}$%.

$\dfrac{15}{2}$% of ₹ 40

$= ₹ \left( 40 \times \dfrac{15}{2 \times 100} \right) \\[1em] = ₹ 40 \times \dfrac{15}{200} \\[1em] = ₹ 40 \times \dfrac{3}{40} \\[1em] = ₹ 3$

Hence, the answer is ₹ 3

(iii) We have:

1% of ₹ 325

$= ₹ \dfrac{1}{100} \times 325 \\[1em] = ₹ 3.25$

Hence, the answer is ₹ 3.25

(iv) We have:

8% of 5 kg

$= \dfrac{8}{100} \times 5 \text{ kg} \\[1em] = \dfrac{40}{100} \text{ kg} \\[1em] = 0.4 \text{ kg} \\[1em] = 400 \text{ g}$

Hence, the answer is 400 g

(v) We have:

$16\dfrac{2}{3}$% of 9 m

Convert to an improper fraction:

$16\dfrac{2}{3}$% = $\dfrac{50}{3}$%

$\dfrac{50}{3}$% of 9 m

$= \left( 9 \times \dfrac{50}{3 \times 100} \right) \text{ m} \\[1em] = 9 \times \dfrac{50}{300} \text{ m} \\[1em] = 9 \times \dfrac{1}{6} \text{ m} \\[1em] = \dfrac{9}{6} \text{ m} \\[1em] = 1.5 \text{ m}$

Hence, the answer is 1.5 m

(vi) We have:

0.6% of 5 km

$= \dfrac{0.6}{100} \times 5 \text{ km} \\[1em] = \dfrac{0.6}{20} \text{ km} \\[1em] = \dfrac{0.6 \times 10}{20 \times 10} \text{ km} \\[1em] = \dfrac{6}{200} \text{ km} \\[1em] = 0.03 \text{ km} \\[1em] = 30 \text{ m}$

Hence, the answer is 30 m

(vii) We have:

$6\dfrac{1}{4}$% of (1 hour 20 min.)

First, convert time to minutes:

1 hour = 60 min

∴ 1 hour 20 min = 60 min + 20 min = 80 min.

Convert mixed to an improper fraction:

$6\dfrac{1}{4}$% = $\dfrac{25}{4}$%

$\dfrac{25}{4}$% of 80 min

$= \left( 80 \times \dfrac{25}{4 \times 100} \right) \text{ min} \\[1em] = 80 \times \dfrac{25}{400} \text{ min} \\[1em] = 80 \times \dfrac{1}{16} \text{ min} \\[1em] = \dfrac{80}{16} \text{ min} \\[1em] = 5 \text{ min}$

Hence, the answer is 5 min

Express:

(i) 56 p as a per cent of ₹ 2.80

(ii) 45 cm as a per cent of 3 m

(iii) 630 g as a per cent of 3.5 kg

(iv) 18 hours as a per cent of 2 days

(v) 2.8 mm as a per cent of 2.24 cm

Answer

(i) 56 p as a per cent of ₹ 2.80

First quantity = 56 p

Convert rupee into paise:

1 rupee = 100 paise

∴ Second quantity = ₹ 2.80 = 2.80 x 100 p = 280 p

Percentage =

$\left( \dfrac{\text{First Quantity}}{\text{Second Quantity}} \times 100 \right)$%

= $\left( \dfrac{56}{280} \times 100 \right)$%

= $\left( \dfrac{1}{5} \times 100 \right)$%

= 20%

Hence, the answer is 20%.

(ii) 45 cm as a per cent of 3 m

First quantity = 45 cm

Convert meter into centimeter:

1 m = 100 cm

∴ Second quantity = 3 m = 3 x 100 cm = 300 cm

Percentage =

$\left( \dfrac{\text{First Quantity}}{\text{Second Quantity}} \times 100 \right)$%

= $\left( \dfrac{45}{300} \times 100 \right)$%

= $\dfrac{45}{3}$%

= 15%

Hence, the answer is 15%

(iii) 630 g as a per cent of 3.5 kg

First quantity = 630 g

Convert kg into grams:

1 kg = 1000 g

∴ Second quantity = 3.5 kg = 3.5 x 1000 g = 3500 g

Percentage =

$\left( \dfrac{\text{First Quantity}}{\text{Second Quantity}} \times 100 \right)$%

= $\left( \dfrac{630}{3500} \times 100 \right)$%

= $\dfrac{630}{35}$%

= 18%

Hence, the answer is 18%

(iv) 18 hours as a per cent of 2 days

First quantity = 18 hours

Convert days into hours:

1 day = 24 hours

∴ Second quantity = 2 days = 2 x 24 hours = 48 hours

Percentage =

$\left( \dfrac{\text{First Quantity}}{\text{Second Quantity}} \times 100 \right)$%

= $\left( \dfrac{18}{48} \times 100 \right)$%

= $\left( \dfrac{3}{8} \times 100 \right)$%

= 37.5%

Hence, the answer is 37.5%

(v) 2.8 mm as a per cent of 2.24 cm

First quantity = 2.8 mm

Convert cm into mm:

1 cm = 10 mm

∴ Second quantity = 2.24 cm = 2.24 x 10 mm = 22.4 mm

Percentage =

$\left( \dfrac{\text{First Quantity}}{\text{Second Quantity}} \times 100 \right)$%

= $\left( \dfrac{2.8}{22.4} \times 100 \right)$%

= $\left( \dfrac{1}{8} \times 100 \right)$%

= 12.5%

Hence, the answer is 12.5%

(i) What per cent of 1.5 m is 60 cm?

(ii) What per cent of 2 kg is 125 g?

(iii) What per cent of ₹ 6 is 40 p?

(iv) What per cent of a day is 10 h?

(v) What per cent of $7\dfrac{1}{3}$m is $5\dfrac{1}{2}$m?

Answer

(i) What per cent of 1.5 m is 60 cm?

Convert m into cm:

1 m = 100 cm

∴ Total = 1.5 x 100 cm = 150 cm

Part = 60 cm

Percentage =

$\left( \dfrac{\text{Part}}{\text{Total}} \times 100 \right)$%

= $\left( \dfrac{60}{150} \times 100 \right)$%

= $\left( \dfrac{60}{30} \times 20 \right)$%

= $\left( \dfrac{2}{1} \times 20 \right)$%

= 40%

Hence, the answer is 40%

(ii) What per cent of 2 kg is 125 g?

Convert kg into grams:

1 kg = 1000 g

∴ Total = 2 kg = 2 x 1000 g = 2000 g

Part = 125 g

Percentage =

$\left( \dfrac{\text{Part}}{\text{Total}} \times 100 \right)$%

= $\left( \dfrac{125}{2000} \times 100 \right)$%

= $\dfrac{125}{20}$%

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

Hence, the answer is $6\dfrac{1}{4}$%

(iii) What per cent of ₹ 6 is 40 p?

Convert rupee into paise:

₹ 1 = 100 paise

∴ Total = ₹ 6 = 6 x 100 p = 600 p

Part = 40 p

Percentage =

$\left( \dfrac{\text{Part}}{\text{Total}} \times 100 \right)$%

= $\left( \dfrac{40}{600} \times 100 \right)$%

= $\left( \dfrac{40}{6} \times 1 \right)$%

= $\dfrac{40}{6}$%

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

Hence, the answer is $6\dfrac{2}{3}$%

(iv) What per cent of a day is 10 h?

Convert day into hours:

1 day = 24 hours

∴ Total = 24 hours

Part = 10 hours

Percentage =

$\left( \dfrac{\text{Part}}{\text{Total}} \times 100 \right)$%

= $\left( \dfrac{10}{24} \times 100 \right)$%

= $\dfrac{125}{3}$%

= $41\dfrac{2}{3}$%

Hence, the answer is $41\dfrac{2}{3}$%

(v) What per cent of $7\dfrac{1}{3}$m is $5\dfrac{1}{2}$m?

First, convert mixed into improper fraction:

$7\dfrac{1}{3} \text{ m} = \dfrac{22}{3}\text{ m}$

$5\dfrac{1}{2} \text{ m} = \dfrac{11}{2}\text{ m}$

Total = $\dfrac{22}{3}\text{ m}$

Part = $\dfrac{11}{2}\text{ m}$

Percentage =

$\left( \dfrac{\text{Part}}{\text{Total}} \times 100 \right)$%

= $\left( \dfrac{\dfrac{11}{2}}{\dfrac{22}{3}} \times 100 \right)$%

= $\left( \dfrac{11}{2} \times \dfrac{3}{22} \times 100 \right)$%

= $\left( \dfrac{1}{2} \times \dfrac{3}{2} \times 100 \right)$%

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

= 75%

Hence, the answer is 75%