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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) 3 : 5 = 9 : ……

\(\frac{3}{5}\) = \(\frac{9}{x}\)

3 × x = 9 × 5

x = \(\frac{9×5}{3}\)

x = 15

3 : 5 = 9 : 15

(ii) 4 : 5 = …… : 10

\(\frac{4}{5}\) = \(\frac{x}{10}\)

5 × x = 4 × 10

x = \(\frac{4×10}{5}\)

x = 8

4 : 5 = 8 : 10

(iii) 6 : …… = 1 : 2

6 : x = 1 : 2

\(\frac{6}{x}\) = \(\frac{1}{2}\)

1 × x = 6 × 2

x = 12

6 : 12 = 1 : 2

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

Hint: \(\frac{21}{15}=\frac{7}{5}=7: 5\)

(ii) True

Hint: \(\frac{3}{5} \times 40=24\)

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) 20 in the ratio 3 : 2.

Dividing 20 into 3 + 2 = 5 equal parts, then

\(20 \times \frac{3}{5}=12\) , \(20 \times \frac{2}{5}=8\)

The required answer is 12, 8

(ii) 27 in the ratio 4 : 5.

Dividing 27 into 4 + 5 = 9 equal parts, and

\(27 \times \frac{4}{9}=12\) , \(27 \times \frac{5}{9}=15\)

The numbers are 12, 15

(iii) 40 in the ratio 6 : 14.

Dividing 40 into 6 + 14 = 20 equal parts and

\(40 \times \frac{6}{20}=12\) , \(40 \times \frac{14}{20}=28\)

The numbers are 12, 28.

Question 7.

In a family, the amount spent in a month for buying Provisions and Vegetables is 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, on dividing 3 + 4 = 7 equal parts,

we get the line segments with lengths

\(\frac{3}{7} \times 63=27 \mathrm{cm}\) , \(\frac{4}{7} \times 63=36 \mathrm{cm}\)

Length of each line segment is 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

Hint: \(\frac{12}{21}=\frac{3 \times 4}{3 \times 7}=\frac{4}{7}\)

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 ₹ 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

Solution:

(c) ₹ 1000

Hint: B’s share = \(\frac{5}{8} \times 1600=1000\)