Well-designed AP 6th Class Maths Guide Chapter 12 Ratio and Proportion Exercise 12.2 offers step-by-step explanations to help students understand problem-solving strategies.
Algebra Class 6 Exercise 12.2 Solutions – 6th Class Maths 12.2 Exercise Solutions
Question 1.
Determine if the following are in proportion.
a) 15, 45, 40, 120
Solution:
15 and 45 = \(\frac { 15 }{ 45 }\) = \(\frac{15 \div 15}{45\div15}\) = \(\frac { 1 }{ 3 }\) = 1 : 3
40 and 120 = \(\frac { 40 }{ 45 }\) = \(\frac{40 \div 40}{120\div 40}\) = \(\frac { 1 }{ 3 }\) = 1 : 3
∴ Since 1 : 3 = 1 : 3
Yes, 15, 45, 40 and 120 are in proportion.
b) 33,121,9,96
Solution:
33 and 121 = \(\frac{33}{121}\) = \(\frac{33 \div 11}{121\div 11}\) = \(\frac { 3 }{ 11 }\) = 3 : 11
9 and 96 = \(\frac{9}{96}\) = \(\frac{9 \div 3}{96\div 3}\) = \(\frac { 3 }{ 32 }\) = 3 : 32
∴ Since 3 : 11 ≠ 3 : 32
No, 33, 121, 9 and 96 are not in proportion.
c) 24,28,36,48
Solution:
24 and 28 = \(\frac{24}{28}\) = \(\frac{24\div 4}{28\div 4}\) = \(\frac { 6 }{ 7 }\) = 6 : 7
36 and 48 = \(\frac{36}{48}\) = \(\frac{36\div 12}{48\div 12}\) = \(\frac { 3 }{ 4 }\) = 3 : 4
∴ Since 6 : 7 ≠ 3 : 4
No, 24, 28, 36 and 48 are not in proportion.
d) 32,48,70,210
Solution:
32 and 48 = \(\frac{36}{48}\) = \(\frac{32\div 16}{48\div 16}\) = \(\frac { 2 }{ 3 }\) = 2 : 3
70 and 210 = \(\frac{70}{210}\) = \(\frac{70\div 70}{210\div 70}\) = \(\frac { 1 }{ 3 }\) = 1 : 3
∴ Since 2 : 3 ≠ 1 : 3
No, 32, 48, 70 and 210 are not in proportion.
e) 4,6,8,12
Solution:
4 and 6 = \(\frac{4}{6}\) = \(\frac{4\div 2}{6\div 2}\) = \(\frac { 2 }{ 3 }\) = 2 : 3
8 and 12 = \(\frac{8}{12}\) = \(\frac{8\div 4}{12\div 4}\) = \(\frac { 2 }{ 3 }\) = 2 : 3
∴ Since 2 : 3 = 2 : 3
Yes, 4,6,8 and 12 are in proportion.
f) 33,44,75,100
Solution:
33 and 44 = \(\frac{33}{44}\) = \(\frac{33\div 11}{44\div 11}\) = \(\frac { 3 }{ 4 }\) = 3 : 4
75 and 100 = \(\frac{75}{100}\) = \(\frac{75\div 25}{100\div 25}\) = \(\frac { 3 }{ 4 }\) = 3 : 4
∴ Since 3 : 4 = 3 : 4
Yes, 33,44,75 and 100 are in proportion.
Question 2.
Write True (T) or False (F) against each of the following statements :
a) 16 : 24 :: 20 : 30
Solution:
16 : 24 :: 20 : 30
16 : 24 = \(\frac{16}{24}\) = 2 : 3
20 : 30 = \(\frac{20}{30}\) = 2 : 3
2 : 3 = 2 : 3
∴ The given statement (a) is True
b) 21 : 6 :: 35 : 10
Solution:
21 : 6 :: 35 : 10
21 : 6 = \(\frac { 1 }{ 2 }\) ⇒ \(\frac { 1 }{ 2 }\) = 7 : 2
35 : 10 = \(\frac { 35 }{ 10 }\) ⇒ \(\frac { 7 }{ 2 }\) = 7 : 2
7 : 2 = 7 : 2
∴ The given statement (b) is True
c) 12 : 8 :: 28 : 12
Solution:
12 : 18 = \(\frac { 12 }{ 18 }\) = 2 : 3
28 : 12 = \(\frac { 28 }{ 12 }\) ⇒ \(\frac { 7 }{ 3 }\) = 7 : 3
2 : 3 = 7 : 3
∴ The given statement (c) is False
∴ The given statement (c) is False
d) 8 : 9 :: 24 : 27
Solution:
24 : 27 = \(\frac { 24 }{ 27 }\) = 8 : 9
8 : 9 = 8 : 9
∴ The given statement (d) is True
e) 5.2 : 3.9 :: 3 : 4
Solution:
5.2 : 3.9 = \(\frac { 5.2 }{ 3.9 }\) = \(\frac{5.2 \times 10}{3.9 \times 10}\) = \(\frac { 52 }{ 39 }\) ⇒ \(\frac { 4 }{ 3 }\) = 4 : 3
4 : 3 ≠ 3 : 4
∴ The given statement (e) is false
∴ The given statement (e) is False
f) 0.9 : 0.36 :: 10 : 4
Solution:
0.9 : 0.36 :: 10 : 4
5 : 2 = 5 : 2.
∴ The given statement (f) is True
Question 3.
Are the following statements true ?
a) 40 persons : 200 persons = ₹ 15 : ₹ 75
Solution:
40 persons : 200 persons
= \(\frac { 40 }{ 200 }\) = \(\frac{40 \div 40}{200 \div 40}\) = \(\frac { 1 }{ 5 }\) = 1 : 5
₹ 15 : ₹ 75 = \(\frac { 15 }{ 75 }\) = \(\frac{15 \div 15}{75 \times 15}\) = \(\frac { 1 }{ 5 }\) = 1 : 5
∴ Statement (a) is True
b) 7.5 litres : 15 litres = 5 kg : 10 kg
Solution:
7.5 litres : 15 litres
= \(\frac{7.5}{15}\) = \(\frac{75}{150}\) = \(\frac{75 \div 75}{150 \div 75}\) = \(\frac { 1 }{ 2 }\) = 1 : 2
5 kg : 10 kg = \(\frac { 5 }{ 10 }\) = \(\frac{5 \div 5}{10 \div 5}\) = \(\frac { 1 }{ 2 }\) = 1 : 2
∴ Statement (b) is True
c) 99 kg : 45 kg = ₹ 44 : ₹ 20
Solution:
99 kg : 45 kg = \(\frac { 99 }{ 45 }\) = \(\frac{99 \div 9}{45 \div 9}\) = \(\frac { 11 }{ 5 }\) = 11 : 5
₹ 44 : ₹ 20 = \(\frac { 44 }{ 20 }\) = \(\frac{44 \div 4}{20 \div 4}\) = \(\frac { 11 }{ 5 }\) = 11 : 5
∴ Statement (c) is True
d) 32 m : 64 m = 6 sec : 12 sec
Solution:
32 m : 64 m = \(\frac { 32 }{ 64 }\) = \(\frac{32 \div 32}{64 \div 32}\) = \(\frac { 1 }{2 }\) = 1 : 2
6 sec : 12 sec = \(\frac { 6 }{ 12 }\) = \(\frac{6 \div 6}{12 \div 6}\) = \(\frac { 1 }{2 }\) = 1 : 2
∴ Statement (d) is True
e) 45 km 60 km = 12 hours : 15 hours
Solution:
45 km : 60 km = \(\frac { 45 }{ 60 }\) = \(\frac { 45 /div 15 }{60 /div 15 }\) = \(\frac { 3 }{ 4 }\) = 3 : 4
12 hours : 15 hours = \(\frac { 12 }{ 15 }\) = \(\frac { 12 /div 3 }{15 /div 3 }\) = \(\frac { 4 }{ 5 }\) = 4 : 5
Since 3 : 4 ≠ 4 : 5
∴ Statement (e) 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
Solution:
25 cm : 1m = 25 cm : 1000 m [∵ 1m = 100 cm]
= \(\frac { 25 }{ 100 }\) = \(\frac { 25 /div 25 }{100 /div 25 }\) = \(\frac { 1 }{ 4 }\) = 1 : 4
₹ 40 : ₹ 160 = \(\frac { 40 }{ 160 }\) = \(\frac { 40 /div 40 }{ 160 /div 40 }\) = \(\frac { 1 }{ 4 }\) = 1 : 4
∴ The given ratios are in proportion.
Extreme terms are 25 cm and ₹ 160
Middle terms are 1 m and ₹ 40
b) 39 litres : 65 litres and 6 bottles : 10 bottles
Solution:
39 litres : 65 litres = \(\frac { 39 }{ 65 }\) = \(\frac { 39 /div 13 }{ 65 /div 13 }\) = \(\frac { 3 }{ 5 }\) = 3 : 5
6 bottles : 10 bottles = \(\frac { 6 }{ 10 }\) = \(\frac { 6/div 2 }{ 10 /div 2 }\) = \(\frac { 3 }{ 5 }\) = 3 : 5
∴ The given ratios are in proportion.
Extreme terms are 39 litres and 10 bottles
Middle terms are 65 litres and 6 bottles
c) 2 kg : 80 kg and 25 g : 625 g
Solution:
2 kg : 80 kg = \(\frac { 2 }{ 80 }\) = \(\frac { 2/div 2 }{ 80 /div 2 }\) = \(\frac { 1 }{ 40 }\) = 1 : 4
25 g : 625 g = \(\frac { 25 }{ 625 }\) = \(\frac { 25/div 25 }{ 625 /div 25 }\) = \(\frac { 1 }{ 25 }\) = 1: 25
Since 1 : 4 ≠ 1 : 25
∴ The given ratios are not in proportion.
d) 200 ml : 2.5 litre and ₹ 4 : ₹ 50
Soluton:
200 ml : 2.5 litre
= \(\frac { 200 }{ 2500 }\) = \(\frac { 200/div 100 }{ 2500 /div 100 }\) = \(\frac { 2 }{ 25 }\) = 2 : 25
₹ 4 : ₹ 50 = \(\frac { 4 }{ 50 }\) = \(\frac { 4/div 2 }{ 50 /div 2 }\) = \(\frac { 2 }{ 25 }\) = 2 : 25
∴ The given ratios are in proportion.
Extreme terms are 200 ml and ₹ 50
Middle terms are 2.5 litre and ₹ 4