6th Maths : Term 1 Unit 3
Ratio and Proportion - Exercise 3.2
1. Fill in the blanks of the given equivalent ratios.
(i) \(3 : 5 = 9 : \_\_\_\)
(ii) \(4 : 5 = \_\_\_\ : 10\)
(iii) \(6 : \_\_\_\ = 1 : 2\)
Answer:
(i) 15 (ii) 8 (iii) 12
2. Complete the table.
3. Say True or False.
(i) \(5 : 7\) is equivalent to \(21 : 15\) [False]
(ii) If \(40\) is divided in the ratio \(3 : 2\), then the larger part is \(24\). [True]
4. Give two equivalent ratios for each of the following.
(i) \(3 : 2\)
(ii) \(1 : 6\)
(iii) \(5 : 4\)
Solution:
(i) \(3 : 2\)
Fractional form = \(\frac{3}{2}\)
Equivalent ratios: \(\frac{3}{2} \times \frac{2}{2} = \frac{6}{4}\) and \(\frac{3}{2} \times \frac{3}{3} = \frac{9}{6}\).
Answers: \(6 : 4, 9 : 6\)
(ii) \(1 : 6\)
Fractional form = \(\frac{1}{6}\)
Equivalent ratios: \(\frac{1}{6} \times \frac{2}{2} = \frac{2}{12}\) and \(\frac{1}{6} \times \frac{3}{3} = \frac{3}{18}\).
Answers: \(2 : 12, 3 : 18\)
(iii) \(5 : 4\)
Fractional form = \(\frac{5}{4}\)
Equivalent ratios: \(\frac{5}{4} \times \frac{2}{2} = \frac{10}{8}\) and \(\frac{5}{4} \times \frac{3}{3} = \frac{15}{12}\).
Answers: \(10 : 8, 15 : 12\)
Fractional form = \(\frac{3}{2}\)
Equivalent ratios: \(\frac{3}{2} \times \frac{2}{2} = \frac{6}{4}\) and \(\frac{3}{2} \times \frac{3}{3} = \frac{9}{6}\).
Answers: \(6 : 4, 9 : 6\)
(ii) \(1 : 6\)
Fractional form = \(\frac{1}{6}\)
Equivalent ratios: \(\frac{1}{6} \times \frac{2}{2} = \frac{2}{12}\) and \(\frac{1}{6} \times \frac{3}{3} = \frac{3}{18}\).
Answers: \(2 : 12, 3 : 18\)
(iii) \(5 : 4\)
Fractional form = \(\frac{5}{4}\)
Equivalent ratios: \(\frac{5}{4} \times \frac{2}{2} = \frac{10}{8}\) and \(\frac{5}{4} \times \frac{3}{3} = \frac{15}{12}\).
Answers: \(10 : 8, 15 : 12\)
5. Which of the two ratios is larger?
(i) \(4 : 5\) or \(8 : 15\)
(ii) \(3 : 4\) or \(7 : 8\)
(iii) \(1 : 2\) or \(2 : 1\)
Solution:
(i) \(4 : 5\) (or) \(8 : 15\)
\(\frac{4}{5} \times \frac{3}{3} = \frac{12}{15}\) and \(\frac{8}{15}\).
Comparing: \(\frac{12}{15} > \frac{8}{15}\). Conclusion: \(4 : 5\) is greater.
(ii) \(3 : 4\) (or) \(7 : 8\)
\(\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}\) and \(\frac{7}{8}\).
Comparing: \(\frac{6}{8} < \frac{7}{8}\). Conclusion: \(7 : 8\) is greater.
(iii) \(1 : 2\) (or) \(2 : 1\)
\(\frac{1}{2}\) and \(\frac{2}{1} = \frac{4}{2}\).
Comparing: \(\frac{1}{2} < \frac{4}{2}\). Conclusion: \(2 : 1\) is greater.
\(\frac{4}{5} \times \frac{3}{3} = \frac{12}{15}\) and \(\frac{8}{15}\).
Comparing: \(\frac{12}{15} > \frac{8}{15}\). Conclusion: \(4 : 5\) is greater.
(ii) \(3 : 4\) (or) \(7 : 8\)
\(\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}\) and \(\frac{7}{8}\).
Comparing: \(\frac{6}{8} < \frac{7}{8}\). Conclusion: \(7 : 8\) is greater.
(iii) \(1 : 2\) (or) \(2 : 1\)
\(\frac{1}{2}\) and \(\frac{2}{1} = \frac{4}{2}\).
Comparing: \(\frac{1}{2} < \frac{4}{2}\). Conclusion: \(2 : 1\) is greater.
6. Divide the numbers given below in the required ratio.
(i) \(20\) in the ratio \(3 : 2\)
(ii) \(27\) in the ratio \(4 : 5\)
(iii) \(40\) in the ratio \(6 : 14\)
Solution:
(i) Ratio \(3 : 2\): Total parts = \(5\).
\(20 \times \frac{3}{5} = 12\); \(20 \times \frac{2}{5} = 8\). Result: \(12 : 8\).
(ii) Ratio \(4 : 5\): Total parts = \(9\).
\(27 \times \frac{4}{9} = 12\); \(27 \times \frac{5}{9} = 15\). Result: \(12 : 15\).
(iii) Ratio \(6 : 14\): Total parts = \(20\).
\(40 \times \frac{6}{20} = 12\); \(40 \times \frac{14}{20} = 28\). Result: \(12 : 28\).
\(20 \times \frac{3}{5} = 12\); \(20 \times \frac{2}{5} = 8\). Result: \(12 : 8\).
(ii) Ratio \(4 : 5\): Total parts = \(9\).
\(27 \times \frac{4}{9} = 12\); \(27 \times \frac{5}{9} = 15\). Result: \(12 : 15\).
(iii) Ratio \(6 : 14\): Total parts = \(20\).
\(40 \times \frac{6}{20} = 12\); \(40 \times \frac{14}{20} = 28\). Result: \(12 : 28\).
7. In a family, the amount spent in a month for buying Provisions and Vegetables are in the ratio \(3 : 2\). If the allotted amount is ₹4000, then what will be the amount spent for (i) Provisions and (ii) Vegetables?
Solution:
Total amount = ₹4000. Ratio = \(3 : 2\). Total parts = \(5\).
(i) Provisions \(\Rightarrow 4000 \times \frac{3}{5} = ₹2400\)
(ii) Vegetables \(\Rightarrow 4000 \times \frac{2}{5} = ₹1600\)
(i) Provisions \(\Rightarrow 4000 \times \frac{3}{5} = ₹2400\)
(ii) Vegetables \(\Rightarrow 4000 \times \frac{2}{5} = ₹1600\)
8. A line segment \(63\text{ cm}\) long is to be divided into two parts in the ratio \(3 : 4\). Find the length of each part.
Solution:
Length = \(63\text{ cm}\). Ratio = \(3 : 4\). Total parts = \(7\).
Length of part I \(= 63 \times \frac{3}{7} = 27\text{ cm}\).
Length of part II \(= 63 \times \frac{4}{7} = 36\text{ cm}\).
Length of part I \(= 63 \times \frac{3}{7} = 27\text{ cm}\).
Length of part II \(= 63 \times \frac{4}{7} = 36\text{ cm}\).
Objective Type Questions
9. If \(2 : 3\) and \(4 : \_\_\_\) are equivalent ratios, then the missing term is
(a) 6
(b) 2
(c) 4
(d) 3
10. An equivalent ratio of \(4 : 7\) is
(a) 1 : 3
(b) 8 : 15
(c) 14 : 8
(d) 12 : 21
11. Which is not an equivalent ratio of \(\frac{16}{24}\) ?
(a) 6/9
(b) 12/18
(c) 10/15
(d) 20/28
12. If ₹1600 is divided among A and B in the ratio \(3 : 5\) then, B’s share is
(a) ₹480
(b) ₹800
(c) ₹1000
(d) ₹200
Quick Answer Key: Exercise 3.2
1) (i) 15 (ii) 8 (iii) 12 | 2) (i) 36 inches, 6 Feet (ii) 14 days, 9 weeks
3) (i) False (ii) True | 4) (i) 6:4, 9:6 (ii) 2:12, 3:18 (iii) 10:8, 15:12
5) (i) 4:5 is larger (ii) 7:8 is larger (iii) 2:1 is larger
6) (i) 12, 8 (ii) 12, 15 (iii) 12, 28 | 7) (i) ₹2400 (ii) ₹1600
8) 27 cm, 36 cm | 9) (a) | 10) (d) | 11) (d) | 12) (c)