These NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.2 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2
Question 1.
Determine if the following are in proportion.
(a) 15, 45 ; 40, 120
(b) 33, 121; 9, 96
(c) 24, 28, 36, 48
(d) 32,48 :70,210
(e) 4, 6 ; 8, 12
(f) 33, 44 ; 75, 100
Answer:
(a) 15 : 45 = \(\frac{15}{45}=\frac{1}{3}\) = 1 : 3
40 : 120 = \(\frac{40}{120}=\frac{1}{3}\) = 1 : 3
Since, 15 : 45 = 40 : 120
Therefore, 15,45,40,120 are in proportion.
(b) 33 : 121= \(\frac{33}{121}=\frac{3}{11}\) = 3 : 11
9 : 96 = \(\frac{9}{96}=\frac{3}{32}\) = 3 : 32
Since, 33 : 121 ≠ 9 : 96
Therefore, 33,121,9,96 are not in proportion.
(c) 24 : 28 = \(\frac{24}{28}=\frac{6}{7}\) = 6 : 7
36 : 48 = \(\frac{36}{48}=\frac{3}{4}\) = 3 : 4
Since, 24 : 28 ≠ 36 : 48
Therefore, 24, 28,36, 48 are not in proportion.
(d) 32 : 48 = \(\frac{32}{48}=\frac{2}{3}\) = 2 : 3
70 : 210= \(\frac{70}{210}=\frac{1}{3}\) = 1 : 3
Since, 32 : 48 ≠ 70 : 210
Therefore, 32,48, 70, 210 are not in proportion.
(e) 4 : 6 = \(\frac{4}{6}=\frac{2}{3}\) = 2 : 3
8 : 12 = \(\frac{8}{12}=\frac{2}{3}\) = 2 : 3
Since, 4 : 6 = 8 : 12
Therefore, 4,6,8,12 are in proportion.
(f) 33 : 44 = \(\frac{33}{44}=\frac{3}{4}\) = 3 : 4
75 : 100 = \(\frac{75}{100}=\frac{3}{4}\) = 3 : 4
Since, 33 : 44 = 75 : 100
Therefore, 33, 44, 75,100 are in ratio.
Question 2.
Write True (T) or False (F) against each of the following statements:
(a) 16 : 24 :: 20 : 30
(b) 21: 6:: 35 : 10
(c) 12: 18:: 28:12
(d) 8:9:: 24: 27
(e) 5.2 : 3.9 :: 3 :4
(f) 0.9 : 0.36 :: 10 : 4
Answer:
(a) 16 : 24 :: 20 : 30
⇒ \(\frac{16}{24}=\frac{20}{30}\) ⇒ \(\frac{2}{3}=\frac{2}{3}\)
Hence, it is true.
(b) 21 : 6 :: 35 : 10
⇒ \(\frac{21}{6}=\frac{35}{10}\) ⇒ \(\frac{7}{2}=\frac{7}{2}\)
Hence, it is true.
(c) 12 : 18 :: 28 : 12
⇒ \(\frac{12}{18}=\frac{28}{12}\) ⇒ \(\frac{2}{3} \neq \frac{7}{3}\)
Hence, it is false.
(d) 8 : 9 :: 24 : 27
⇒ \(\frac{8}{9}=\frac{24}{27}\) ⇒ \(\frac{8}{9}=\frac{8}{9}\)
Hence, it is true.
(e) 5.2 : 3.9 :: 3 : 4
⇒ \(\frac{5.2}{3.9}=\frac{3}{4}\) ⇒ \(\frac{4}{3} \neq \frac{3}{4}\)
Hence, it is false.
(f) 0.9 : 0.36 :: 10 : 4
⇒ \(\frac{0.9}{0.36}=\frac{10}{4}\) ⇒ \(\frac{5}{2}=\frac{5}{2}\)
Hence, it is true.
Question 3.
Are the following statements true?
(a) 40 persons : 200 persons = ₹ 15: ₹ 75
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
(c) 99 kg : 45 kg = ₹ 44 : ₹ 20
(d) 32 m : 64 m = 6 sec : 12 sec
(e) 45 km : 60 km = 12 hours : 15 hours
Answer:
(a) 40 persons : 200 persons
= \(\frac{40}{200}=\frac{1}{5}\) = 1 : 5
₹ 15 : ₹ 75 = \(\frac{15}{75}=\frac{1}{5}\) = 1 : 5
Since, 40 persons : 200 persons = ₹ 15 : ₹ 75
Hence, the statement is true.
(b) 7.5 litres : 15 litres
= \(\frac{7.5}{15}=\frac{75}{150}=\frac{1}{2}\) = 1 : 2
5 kg : 10 kg = \(\frac{5}{10}=\frac{1}{2}\) = 1 : 2
Since, 7.5 litres : 15 litres = 5 kg: 10 kg
Hence, the statement is true.
(c) 99 kg : 45 kg = \(\frac{99}{45}=\frac{11}{5}\) = 11 : 5
₹ 44 : ₹ 20= \(\frac{44}{20}=\frac{11}{5}\) = 11 : 5
Since, 99 kg: 45 kg = ₹ 44 : ₹ 20 Hence, the statement is true.
(d) 32 m : 64 m = \(\frac{32}{64}=\frac{1}{2}\) = 1 : 2
6 sec : 12 sec = \(\frac{6}{12}=\frac{1}{2}\) = 1 : 2
Since, 32 m : 64 m = 6 sec : 12 sec Hence, the statement is true.
(e) 45 km : 60 km = \(\frac{45}{60}=\frac{3}{4}\) = 3 : 4
12 hours : 15 hours
= \(\frac{12}{15}=\frac{4}{5}\) = 4 : 5
Since, 45 km : 60 km ≠ 12 hours : 15 hours
Hence, the statement is not true.
Question 4.
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and ₹ 40: ₹ 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) 2 kg: 80 kg and 25 g : 625 g
(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50
Answer:
(a) 25 cm : 1 m = 25 cm : (1 × 100) cm
= 25 cm : 100 cm
= \(\frac{25}{100}=\frac{1}{4}\) = 1 : 4
₹ 40 : ₹ 160 = \(\frac{40}{160}=\frac{1}{4}\) = 1 : 4
Since, the ratios are equal, therefore these are in proportion.
Middle terms = 1 m, ₹ 40 and
Extreme terms = 25 cm, ₹ 160
(b) 39 litres : 65 litres
= \(\frac{39}{65}=\frac{3}{5}\) = 3 : 5
6 bottles : 10 bottles
= \(\frac{6}{10}=\frac{3}{5}\) = 3 : 5
Since, the ratios are equal, therefore these are in proportion.
Middle terms = 65 litres, 6 bottles and Extreme terms = 39 litres, 10 bottles
(c) 2 kg : 80 kg = \(\frac{2}{80}=\frac{1}{40}\) = 1 : 40
25 g : 625 g = \(\frac{25}{625}=\frac{1}{25}\) = 1 : 25
Since, the ratios are not equal, therefore these are not in proportion,
(d) 200 ml : 2.5 litres = 200 ml: (25000) litres = 200 ml : 2500 ml = \(\frac{200}{2500}=\frac{2}{25}\) = 2 : 25
₹ 4: ₹ 50 = \(\frac{4}{50}=\frac{2}{25}\) = 2 : 25
Since, the ratios are equal, therefore these are in proportion.
Middle terms = 2.5 litres, ₹ 4 and Extreme terms = 200 ml, ₹ 50