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## Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Question 1.

Fill in the blanks of the given equivalent ratios.

(i) 3 : 5 = 9 : ___

(ii) 4 : 5 = ___ : 10

(iii) 6 : ____ = 1 : 2

Solution:

(i) 15

Hint: \(\frac{3}{5}=\frac{3 \times 3}{5 \times 3}=\frac{9}{15}\)

(ii) 8

Hint: \(\frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}\)

(iii) 12

Hint: \(\frac{1}{2}=\frac{1 \times 6}{2 \times 6}=\frac{6}{12}\)

Question 2.

Complete the Table:

Solution:

Question 3.

Say True or False.

(i) 5 : 7 is equivalent to 21 : 15.

(ii) If 40 is divided in the ratio 3 : 2, then the larger part is 24.

Solution:

(i) False

(ii) True

Question 4.

Give two equivalent ratios for each of the following.

(i) 3 : 2

(ii) 1 : 6

(iii) 5 : 4

Solution:

Question 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:

Question 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

Sum of the ratio = 3 + 2 = 5

5 parts = 20

1 part = \(\frac{20}{5}\)

= 4

3 parts = 3 × 4 = 12

2 parts = 2 × 4 = 8

20 can be divided in the form as 12, 8.

(ii) Ratio = 4 : 5

Sum of the ratio = 4 + 5 = 9

9 parts = 27

1 part = \(\frac{27}{9}\) = 3

4 parts = 4 × 3 = 12

5 parts = 5 × 3 =15

27 can be divided in the form as 12, 15.

(iii) 40 in the ratio 6 : 14

Ratio = 6 : 14

Sum of the ratio = 6 + 14 = 20

20 parts = 40

1 part = \(\frac{40}{20}\) = 2

6 parts = 2 × 6 = 12

14 parts = 2 × 14 = 28

40 can be divided in the form as 12, 28.

Question 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:

Dividing the total amount ₹ 4000 into 3 + 2 = 5 equal parts then

(i) For Provisions:

3 out of 5 parts are spent for provisions and 2 out of 5 parts for vegetables.

\(4000 \times \frac{3}{5}=2400\) for provisions

(ii) For vegetables:

\(4000 \times \frac{2}{5}=1600\) for Vegetables.

₹ 2400 spend on provisions and ₹ 1600 spend on Vegetables.

Question 8.

A line segment 63 cm long is to be divided into two parts in the ratio 3 : 4. Find the length of each part.

Solution:

Total length = 63 cm Ratio = 3 : 4

Sum of the ratio = 3 + 4 = 7

7 parts = 63 cm

1 part = \(\frac{63}{7}\) = 9 cm

3 parts = 3 × 9 cm = 27 cm

4 parts = 4 × 9 cm = 36 cm

∴ 63 cm can be divided into the parts as 27 cm and 36 cm.

**Objective Type Questions**

Question 9.

If 2 : 3 and 4 : ___ or equivalent ratios, then the missing term is ____

(a) 6

(b) 2

(c) 4

(d) 3

Solution:

(a) 6

Hint: \(\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6}\)

Question 10.

An equivalent ratio of 4 : 7 is

(a) 1 : 3

(b) 8 : 15

(c) 14 : 8

(d) 12 : 21

Solution:

(d) 12 : 21

Question 11.

Which is not an equivalent ratio of \(\frac{16}{24}\) ?

(a) \(\frac{6}{9}\)

(b) \(\frac{12}{18}\)

(c) \(\frac{10}{15}\)

(d) \(\frac{20}{28}\)

Solution:

(d) \(\frac{20}{28}\)

Hint: \(\frac{16}{24}=\frac{8 \times 2}{8 \times 3}=\frac{2}{3}\)

Question 12.

If Rs 1600 is divided

(a) Rs 480

(b) Rs 800

(c) Rs 1000

(d) Rs 200

Solution:

(c) Rs 1000