NCERT Solution For Class 6, Maths, Chapter 12, Ratio And Proportion, Exercise 12.2 related the True and False of given ratio. Exercise 12.2, Class 6 maths chapter 12 has total four exercises to study.
NCERT Solution For Class 6, Maths, Chapter 12, Ratio And Proportion, Exercise 12.2
Q.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
Ans:
(a) 15, 45, 40, 120
$15\,\,:\,\,45\,\,=\frac{15}{45}\,\,=\,\,\frac{1}{3}\,=\,\,1\,\,:\,\,3\,$
$40\,\,:\,\,120\,\,=\frac{40}{120}\,\,=\,\,\frac{1}{3}\,=\,\,1\,\,:\,\,3\,$
Hence, 15 : 45 = 40 :120
Therefore, 15, 45, 40, 120 are in proportion.
(b) 33, 121, 9,96
$\,33\,\,:\,121\,\,=\frac{33}{121}\,\,=\,\,\frac{3}{11}\,\,=\,\,3\,\,:\,\,11\,$
$\,9\,\,:\,\,96\,\,=\frac{9}{96}\,\,=\,\,\frac{3}{32}\,\,=\,\,3\,\,:\,\,32\,\,$
Hence 33:121 ≠ 9: 96
∴ These are not in a proportion.
(c) 24, 28, 36, 48
$\,\,24\,\,:\,28\,\,=\frac{24}{28}\,\,=\,\,\frac{6}{7}\,\,=\,\,6\,\,:\,\,7$
$\,\,36\,\,:\,\,48\,\,=\frac{36}{48}\,\,=\,\,\frac{6}{8}=\,\,\frac{3}{4}\,\,=\,\,3\,\,:\,\,4$
Hence 24 :28 ≠ 36 : 48
∴ These are not in a proportion.
(d) 32, 48, 70, 210
$\,\,32\,\,:\,\,48\,\,=\frac{32}{48}\,\,=\,\,\frac{2}{3}\,=\,\,2\,\,:\,\,3$
$\,70\,\,:\,\,210\,\,\,=\frac{70}{210}\,=\frac{7}{21}=\,\,\frac{1}{3}\,=\,\,1\,\,\,:\,\,3$
Since, 32 : 48 ≠ 70 : 210
∴ These are not in a proportion.
(e) 4, 6, 8, 12
$\,\,4\,:\,\,6\,=\frac{4}{6}\,\,=\,\,\frac{2}{3}\,=\,\,2\,\,\,:\,\,\,3\,$
$\,\,8\,\,:\,\,12\,\,\,=\frac{8}{12}\,\,=\,\,\frac{2}{3}\,=\,\,2\,\,:\,\,3\,\,$
Since, 4 : 6 = 8 : 12
∴ These are in a proportion.
(f) 33, 44, 75, 100
$\,33\,\,:\,\,44\,=\frac{33}{44}\,\,=\,\,\frac{3}{4}\,=\,3\,:4\,\,\,$
$\,\,75\,\,:\,\,100\,\,=\frac{75}{100}\,\,=\,\,\frac{3}{4}\,=\,\,3\,\,\,:\,\,\,4\,$
Since, 33 : 44 = 75 : 100
∴ These are in a proportion.
Q.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
Ans:
(a) 16 : 24 :: 20 : 30
$\Rightarrow \,\,\,\,\,\,\,\frac{16}{24}\,\,=\,\,\frac{20}{30}$
$\Rightarrow \,\,\,\,\,\,\,\frac{2}{3}\,\,=\,\frac{2}{3}\,$
Hence, 16 : 24 = 20 : 30
Therefore, it is true.
(b) 21: 6 :: 35 : 10
$\Rightarrow \frac{21}{6}\,\,=\,\frac{35}{10}$
$\Rightarrow \,\frac{7}{2}\,\,=\,\frac{7}{2}$
Hence, 21: 6 = 35 : 10
Therefore, it is true.
(c) 12 : 18 :: 28 : 12
$\Rightarrow \,\frac{12}{18}\,\,=\frac{28}{12}$
$\Rightarrow \,\frac{2}{3}\,\,\ne \,\frac{7}{3}\,$
Hence, 12 : 18 ≠ 28 : 12
Therefore, it is false.
(d) 8 : 9 :: 24 : 27
$\Rightarrow \,\,\,\,\,\,\,\frac{8}{9}\,\,=\,\,\frac{24}{27}$
$\Rightarrow \,\,\,\,\,\,\,\frac{8}{9}\,\,=\,\frac{8}{9}$
Hence, 8 : 9 = 24 : 27
Therefore, it is true.
(e) 5.2 : 3.9 :: 3 : 4
$\Rightarrow \,\,\,\,\,\,\,\frac{5.2}{3.9}\,\,=\,\,\frac{3}{4}$
$\Rightarrow \,\,\,\,\,\,\,\frac{4}{3}\,\,\ne \,\,\frac{3}{4}\,$
Hence, 5.2 : 3.9 ≠ 3 : 4
Therefore, it is false.
(f) 0.9 : 0.36 :: 10 : 4
$\Rightarrow \,\,\,\,\,\,\,\frac{0.9}{0.36}\,\,=\,\,\frac{10}{4}$
$\Rightarrow \,\,\,\,\,\,\,\frac{10}{4}\,\,=\,\,\frac{10}{4}\,$
$\Rightarrow \,\,\,\,\,\,\,\frac{5}{2}\,\,=\,\,\frac{5}{2}$
Hence, 0.9 : 0.36 = 10 : 4
Therefore, it is true.
Q.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
Ans:
(a) 40 persons : 200 persons = ₹ 15 : ₹ 75
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 = 5 kg : 10 kg
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 = ₹ 44 : ₹ 20
99 kg : 45 kg $=\,\frac{99}{45}\,\,=\,\frac{11}{5}=1\,1\,\,:\,\,5$
₹ 44 : ₹ 20 $=\,\frac{44}{20}\,\,=\,\frac{11}{5}=1\,1\,\,:\,\,5$
Since, 99 kg : 45 kg = ₹ 44 : ₹ 20
Hence, the statement is true.
(d) 32 m : 64 m = 6 sec : 12 sec
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 = 12 hours : 15 hours
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.
Q.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
Ans:
(a) 25 cm: 1 m and ₹ 40 : ₹ 160
25 cm : 1 m
⟹ 25 cm : 1 x 100 cm [∵ 1 m = 100 cm]
⟹ 25 cm : 100 cm
⟹ $\frac{25}{100}=\frac{1}{4}=\,\,1:\,\,4$
₹ 40 : ₹ 160
⟹ $\frac{40}{160}=\frac{4}{16}=\frac{1}{4}=\,\,1:\,\,4$
Since, 25 cm: 1 m = ₹ 40 : ₹ 160
Yes, these are in a proportion
Middle terms are 1 m, ₹ 40 and Extreme terms are 25 cm, ₹ 160.
(b) 39 litres: 65 litres and 6 bottles: 10 bottles
39 litres: 65 litres
⟹ $\frac{39}{65}=\frac{39\,\div \,13}{65\,\div \,13}=\frac{3}{5}=\,\,3:\,\,5$
6 bottles: 10 bottles
⟹ $\frac{6}{10}=\frac{3}{5}=\,\,3:\,\,5$
Since, ratios are equal, therefore these are in proportion.
Middle terms are 65 litres, 6 bottles and Extreme terms are 39 litres, 10 bottles
(c) 2 kg : 80 kg and 25 g : 625 g
2 kg : 80 kg
⟹ $\frac{2}{80}=\frac{1}{40}=\,\,1:\,\,40$
25 g : 625 g
⟹ $\frac{25}{625}=\frac{25\,\div \,25}{625\,\div \,25}=\frac{1}{25}=\,\,1:\,\,25$
Since, ratios are not equal, therefore these are not in proportion.
(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50
200 mL : 2.5 litre
⟹ 200 ml : 2.5 x 1000 ml [∵ 1 Litre = 1000 ml]
$\Rightarrow \,\,\,\,\,\,\,\,\,\,200\,\,ml\,\,\,\,:\,\,\frac{25}{10}\times \,1000\,\,ml$
$\Rightarrow \,\,\,\,\,\,\,\,\,200\,\,ml\,\,\,\,:\,\,\,2500\,\,ml $
$\Rightarrow \,\,\,\,\,\,\,\,\,\frac{200}{2500}\,\,\,=\,\,\frac{2}{25}=\,\,2\,\,:\,\,25\,$
₹ 4 : ₹ 50
⟹ $\frac{4}{50}=\frac{2}{25}=\,\,2:\,\,25$
Yes, these are in a proportion
Middle terms are 2.5 litre, ₹ 4 and Extreme terms are 200 ml, ₹ 50.
Chapter 12, Ratio And Proportion
Return to : NCERT Solutions for class 6 Maths (All Chapters)