Percentage — Exercise 10(B)

Find the value of:

16% of 175

Answer

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

⇒ 16% of 175

$\Rightarrow \dfrac{16}{100} \times 175\\[1em] \Rightarrow \dfrac{2800}{100}\\[1em] \Rightarrow 28$

Hence, 16% of 175 = 28.

Find the value of:

140% of 45

Answer

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

⇒ 140% of 45

$\Rightarrow \dfrac{140}{100} \times 45\\[1em] \Rightarrow \dfrac{6300}{100}\\[1em] \Rightarrow 63$

Hence, 140% of 45 = 63.

Find the value of:

2% of 120

Answer

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

⇒ 2% of 120

$\Rightarrow \dfrac{2}{100} \times 120\\[1em] \Rightarrow \dfrac{240}{100}\\[1em] \Rightarrow 2.4$

Hence, 2% of 120 = 2.4.

Find the value of:

12.5% of 72

Answer

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

⇒ 12.5% of 72

$\Rightarrow \dfrac{12.5}{100} \times 72\\[1em] \Rightarrow \dfrac{900}{100}\\[1em] \Rightarrow 9$

Hence, 12.5% of 72 = 9.

Find the value of:

14% of 14

Answer

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

⇒ 14% of 14

$\Rightarrow \dfrac{14}{100} \times 14\\[1em] \Rightarrow \dfrac{196}{100}\\[1em] \Rightarrow 1.96$

Hence, 14% of 14 = 1.96.

Find the value of:

$16\dfrac{2}{3}$% of 18

Answer

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

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

⇒ $\dfrac{50}{3}$% of 18

$\Rightarrow \dfrac{50}{3 \times 100} \times 18\\[1em] \Rightarrow \dfrac{50 \times 18}{300}\\[1em] \Rightarrow \dfrac{900}{300}\\[1em] \Rightarrow 3$

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

Find the value of:

5% of 12.6

Answer

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

⇒ 5% of 12.6

$\Rightarrow \dfrac{5}{100} \times 12.6\\[1em] \Rightarrow \dfrac{63}{100}\\[1em] \Rightarrow 0.63$

Hence, 5% of 12.6 = 0.63.

Find the value of:

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

Answer

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

⇒ 20% of $\dfrac{1}{3}$

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

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

Find the value of:

14% of ₹ 75

Answer

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

⇒ 14% of ₹ 75

$\Rightarrow \dfrac{14}{100} \times 75\\[1em] \Rightarrow \dfrac{1050}{100}\\[1em] \Rightarrow ₹\ 10.50$

Hence, 14% of ₹ 75 = ₹ 10.50.

Find the value of:

60% of 50 kg

Answer

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

⇒ 60% of 50 kg

$\Rightarrow \dfrac{60}{100} \times 50\\[1em] \Rightarrow \dfrac{3000}{100}\\[1em] \Rightarrow 30 \text{ kg}$

Hence, 60% of 50 kg = 30 kg.

Find the value of:

8% of 65 cm

Answer

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

⇒ 8% of 65 cm

$\Rightarrow \dfrac{8}{100} \times 65\\[1em] \Rightarrow \dfrac{520}{100}\\[1em] \Rightarrow 5.2 \text{ cm}$

Hence, 8% of 65 cm = 5.2 cm.

Find the value of:

5% of 3 kg

Answer

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

$\Rightarrow \dfrac{5}{100} \times 3000\\[1em] \Rightarrow \dfrac{15000}{100}\\[1em] \Rightarrow 150 \text{ g}$

Hence, 5% of 3 kg = 150 g.

Find the value of:

10% of 1 litre

Answer

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

$\Rightarrow \dfrac{10}{100} \times 1000\\[1em] \Rightarrow \dfrac{10000}{100}\\[1em] \Rightarrow 100 \text{ ml}$

Hence, 10% of 1 litre = 100 ml.

Find the value of:

40% of 1 year

Answer

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

$\Rightarrow \dfrac{40}{100} \times 365\\[1em] \Rightarrow \dfrac{14600}{100}\\[1em] \Rightarrow 146 \text{ days}$

Hence, 40% of 1 year = 146 days.

Find the value of:

9% of 1 m

Answer

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

$\Rightarrow \dfrac{9}{100} \times 100\\[1em] \Rightarrow 9 \text{ cm}$

Hence, 9% of 1 m = 9 cm.

What per cent of 95 is 19?

Answer

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

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

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

= 20%

Hence, 19 is 20% of 95.

What per cent of 40 is 32?

Answer

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

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

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

= 80%

Hence, 32 is 80% of 40.

What per cent of 65 is 117?

Answer

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

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

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

= 180%

Hence, 117 is 180% of 65.

What per cent of 42 is 29.4?

Answer

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

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

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

= 70%

Hence, 29.4 is 70% of 42.

What per cent is 43 p of ₹ 1?

Answer

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

We know, ₹ 1 = 100 paise.

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

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

= 43%

Hence, 43 p is 43% of ₹ 1.

What per cent is 16 mm of 1 cm?

Answer

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

We know, 1 cm = 10 mm.

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

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

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

= 160%

Hence, 16 mm is 160% of 1 cm.

What per cent is 8 cm of 1 m?

Answer

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

We know, 1 m = 100 cm.

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

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

= 8%

Hence, 8 cm is 8% of 1 m.

What per cent is 635 m of 1 km?

Answer

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

We know, 1 km = 1000 m.

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

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

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

= 63.5%

Hence, 635 m is 63.5% of 1 km.

What per cent is 27 p of ₹ 1.80?

Answer

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

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

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

= 15%

Hence, 27 p is 15% of ₹ 1.80.

What per cent is 48 cm of 1.5 m?

Answer

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

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

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

= 32%

Hence, 48 cm is 32% of 1.5 m.

What per cent is 175 gm of 2.5 kg?

Answer

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

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

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

= 7%

Hence, 175 gm is 7% of 2.5 kg.

What per cent is 2 minutes 24 seconds of 1 hour?

Answer

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

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

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

= 4%

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

What per cent is 189 m of 1.05 km?

Answer

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

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

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

= 18%

Hence, 189 m is 18% of 1.05 km.

What is the number whose 8% is 18?

Answer

Let the required number be x.

8% of x = 18

$\Rightarrow \dfrac{8}{100} \times x = 18\\[1em] \Rightarrow x = \dfrac{18 \times 100}{8}\\[1em] \Rightarrow x = \dfrac{1800}{8}\\[1em] \Rightarrow x = 225$

Hence, the required number is 225.

What is the number whose 6% is 8.1?

Answer

Let the required number be x.

6% of x = 8.1

$\Rightarrow \dfrac{6}{100} \times x = 8.1\\[1em] \Rightarrow x = \dfrac{8.1 \times 100}{6}\\[1em] \Rightarrow x = \dfrac{810}{6}\\[1em] \Rightarrow x = 135$

Hence, the required number is 135.

What is the amount whose 12% is ₹ 21?

Answer

Let the required amount be ₹ x.

12% of x = 21

$\Rightarrow \dfrac{12}{100} \times x = 21\\[1em] \Rightarrow x = \dfrac{21 \times 100}{12}\\[1em] \Rightarrow x = \dfrac{2100}{12}\\[1em] \Rightarrow x = 175$

Hence, the required amount is ₹ 175.

What is the length whose 16% is 36 cm?

Answer

Let the required length be x cm.

16% of x = 36

$\Rightarrow \dfrac{16}{100} \times x = 36\\[1em] \Rightarrow x = \dfrac{36 \times 100}{16}\\[1em] \Rightarrow x = \dfrac{3600}{16}\\[1em] \Rightarrow x = 225$

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

What is the number whose 12.5% is 3.5?

Answer

Let the required number be x.

12.5% of x = 3.5

$\Rightarrow \dfrac{12.5}{100} \times x = 3.5\\[1em] \Rightarrow x = \dfrac{3.5 \times 100}{12.5}\\[1em] \Rightarrow x = \dfrac{350}{12.5}\\[1em] \Rightarrow x = 28$

Hence, the required number is 28.