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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 = \(\frac{5}{8} \times 1600=1000\)