Ncert Solutions For Class 6 Maths Ex 12.2

Ncert Solutions For Class 6 Maths Chapter 12 Ex 12.2

Questsion 1:

Find whether the following set of numbers are in proportion.

i) 15, 45, 40, 120 ii) 33, 121, 9, 96

iii) 4, 6, 8, 12 iv) 33, 44, 75, 100

Solution:

i) 15, 45, 40, 120

$$\frac{15}{45}\, =\, \frac{1}{3}$$ $$\frac{40}{120}\, =\, \frac{1}{3}$$

∴ 15, 45, 40, 120 are in proportion.

ii) 33, 121, 9, 96

$$\frac{33}{121}\, =\, \frac{3}{11}$$ $$\frac{9}{96}\, =\, \frac{3}{32}$$

∴ 33, 121, 9, 96 are not in proportion.

iii) 4, 6, 8, 12

$$\frac{4}{6}\, =\, \frac{2}{3}$$ $$\frac{8}{12}\, =\, \frac{2}{3}$$

∴ 4, 6, 8, 12 are in proportion.

iv) 33, 44, 75, 100

$$\frac{33}{44}\, =\, \frac{3}{4}$$ $$\frac{75}{100}\, =\, \frac{3}{4}$$

∴ 33, 44, 75, 100 are in proportion.

Questsion 2:

State whether the following statements are true or false.

i) 16:24::20:30 ii) 21:6::35:10

iii)12:18::28:12 iv) 8:9::24:27

v) 5.2:3.9::3:4 vi) 0.9:0.36::10:4

Solution:

i) $$\frac{16}{24}\, =\, \frac{2}{3}$$

$$\frac{20}{30}\, =\, \frac{2}{3}$$

∴ $$\frac{16}{24}\, =\, \frac{20}{30}$$

True

ii) $$\frac{21}{6}\, =\, \frac{7}{2}$$

$$\frac{35}{10}\, =\, \frac{7}{2}$$

∴ $$\frac{21}{6}\, =\, \frac{35}{10}$$

True

iii) $$\frac{12}{18}\, =\, \frac{2}{3}$$

$$\frac{28}{12}\, =\, \frac{7}{3}$$

∴ $$\frac{12}{18} \, \neq \, \frac{28}{12}$$

False

iv) $$\frac{24}{27}\, =\, \frac{8}{9}$$

True

v) $$\frac{5.2}{3.9}\, =\, \frac{4}{3}$$

∴ $$\frac{4}{3} \, \neq \, \frac{3}{4}$$

False

vi) $$\frac{0.9}{0.36}\, =\, \frac{90}{36}\, =\, \frac{10}{4}$$

True

Questsion 3:

State whether the following statements are true:

a) 200 persons: 40 persons = Rs.75: Rs.15

Solution:

$$\Rightarrow \frac{200}{40}=\frac{5}{1}$$

Similarly

$$\Rightarrow \frac{75}{15}=\frac{5}{1}$$

Both are equal so the statement is true

b) 90 litres: 15 litres = 30kg: 5kg

Solution:

$$\Rightarrow \frac{90}{15}=\frac{6}{1}$$

Similarly

$$\Rightarrow \frac{30}{5}=\frac{6}{1}$$

Both are equal so the statement is true

c) 99 persons: 66 persons = 33 kg: 22kg

Solution:

$$\Rightarrow \frac{99}{66}=\frac{3}{2}$$

Similarly

$$\Rightarrow \frac{33}{22}=\frac{3}{2}$$

Both are equal so the statement is true

d) 8 m: 24m = 11kg: 33kg

Solution:

$$\Rightarrow \frac{8}{24}=\frac{1}{3}$$

Similarly

$$\Rightarrow \frac{11}{33}=\frac{1}{3}$$

Both are equal so the statement is true

e) 32 kg: 64kg = 44m: 20m

Solution:

$$\Rightarrow \frac{32}{64}=\frac{1}{2}$$

Similarly

$$\Rightarrow \frac{44}{20}=\frac{11}{5}$$

Both are not equal so the statement is false

Questsion 4:

Check whether the given ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion

a) 50cm: 2m and Rs.60: Rs.240

Solution:

1m = 100cm

So, 2m = 200cm

$$\Rightarrow \frac{50}{200}=\frac{1}{4}$$

Similarly

$$\Rightarrow \frac{60}{240}=\frac{1}{4}$$

The ratios are equal and therefore these are in proportion

Middle terms = 200cm, Rs.60

Extreme terms = 50cm, Rs.240

b) 26litres: 39litres and 8bottles: 12bottles

Solution:

$$\Rightarrow \frac{26}{39}=\frac{2}{3}$$

Similarly

$$\Rightarrow \frac{8}{12}=\frac{2}{3}$$

The ratios are equal and therefore these are in proportion

Middle terms = 39litres, 8bottles

Extreme terms = 26litres, 12bottles

c) 4kg: 40kg and 15g: 225g

Solution:

$$\Rightarrow \frac{4}{40}=\frac{1}{10}$$

Similarly

$$\Rightarrow \frac{15}{225}=\frac{1}{15}$$

The ratios are not equal and therefore these are not in proportion

d) 4 persons: 42 persons and Rs.8: Rs.84

Solution:

$$\Rightarrow \frac{4}{42}=\frac{2}{21}$$

Similarly

$$\Rightarrow \frac{8}{84}=\frac{2}{21}$$

The ratios are equal and therefore these are in proportion

Middle terms = 42 persons , Rs.8

Extreme terms = 4 persons, Rs.84