Samacheer Class 6 Maths Ratio and Proportion Book Back Answers & Solutions

Q: Find the simplified form of the following ratios. (i) 15 : 20 (ii) 32 : 24 (iii) 7 : 15 (iv) 12 : 27 (v) 75 : 100

(i) 15 : 20 = \frac{15}{20} = \frac{3}{4} = 3 : 4 (ii) 32 : 24 = \frac{32}{24} = \frac{4}{3} = 4 : 3 (iii) 7 : 15 (iv) 12 : 27 = \frac{12}{27} = \frac{4}{9} = 4 : 9 (v) 75 : 100 = \frac{75}{100} = \frac{3}{4} = 3 : 4

Q: Fill in the blanks of the given equivalent ratios. (i) 3 : 5 = 9 : …… (ii) 4 : 5 = …… : 10 (iii) 6 : …… = 1 : 2

(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}

Q.1Fill in the blanks. (i) Ratio of ₹ 3 to ₹ 5 = ____ (ii) Ratio of 3 m to 200 cm = ______ (iii) Ratio of 5 km 400 m to 6 km = ____ (iv) Ratio of 75 paise to ₹ 2 = ____v

Solution

(i) 3 : 5
(ii) 3 : 2
Hint: 3m = 300 cm
(iii) 9 : 10
Hint: 5km 400 m = 5400m and 6 km = 6000 m
(iv) 3 : 8
Hint: ₹ 2 = 200 paise
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Answer:

(i) 3 : 5
(ii) 3 : 2
Hint: 3m = 300 cm
(iii) 9 : 10
Hint: 5km 400 m = 5400m and 6 km = 6000 m
(iv) 3 : 8
Hint: ₹ 2 = 200 paise
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Q.2Say whether the following statements are True or False. (i) The ratio of 130 cm to 1 m is 13 : 10 (ii) One of the terms in a ratio cannot be 1v

Solution

(i) True
Hint: 1m = 100 cm
(ii) False

Answer:

(i) True
Hint: 1m = 100 cm
(ii) False

Q.3Find the simplified form of the following ratios. (i) 15 : 20 (ii) 32 : 24 (iii) 7 : 15 (iv) 12 : 27 (v) 75 : 100v

Solution

(i) 15 : 20
= \(\frac{15}{20}\)
= \(\frac{3}{4}\)
= 3 : 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1
(ii) 32 : 24
= \(\frac{32}{24}\)
= \(\frac{4}{3}\)
= 4 : 3
(iii) 7 : 15
(iv) 12 : 27
= \(\frac{12}{27}\)
= \(\frac{4}{9}\)
= 4 : 9
(v) 75 : 100
= \(\frac{75}{100}\)
= \(\frac{3}{4}\)
= 3 : 4

Answer:

(i) 15 : 20
= \(\frac{15}{20}\)
= \(\frac{3}{4}\)
= 3 : 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1
(ii) 32 : 24
= \(\frac{32}{24}\)
= \(\frac{4}{3}\)
= 4 : 3
(iii) 7 : 15
(iv) 12 : 27
= \(\frac{12}{27}\)
= \(\frac{4}{9}\)
= 4 : 9
(v) 75 : 100
= \(\frac{75}{100}\)
= \(\frac{3}{4}\)
= 3 : 4

Q.4Akilan walks 10 km in an hour while Selvi walks 6 km in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.v

Solution

Ratio of the distance covered by Akilan to that of Selvi = 10 km : 6 km
= \(\frac{10}{6}\)
= \(\frac{5}{3}\)
= 5 : 3

Answer:

Ratio of the distance covered by Akilan to that of Selvi = 10 km : 6 km
= \(\frac{10}{6}\)
= \(\frac{5}{3}\)
= 5 : 3

Q.5The cost of parking a bicycle is Rs 5 and the cost of parking a scooter is Rs 15. Find the simplest ratio of the parking cost of a bicycle to that of a scooter.v

Solution

Ratio of the parking cost of a bicycle to that of a scooter = Rs 5 : Rs 15
= \(\frac{5}{15}\)
= \(\frac{1}{3}\)
= 1 : 3
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Answer:

Ratio of the parking cost of a bicycle to that of a scooter = Rs 5 : Rs 15
= \(\frac{5}{15}\)
= \(\frac{1}{3}\)
= 1 : 3
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Q.6Out of 50 students in a class, 30 are boys. Find the ratio of (i) number of boys to the number of girls. (ii) the number of girls to the total number of students. (iii) the number of boys to the total number of students.v

Solution

Total no of students = 50
No of boys = 30
No of girls = 50 – 30 = 20
(i) Ratio of boys to girls = 30 : 20
= \(\frac{30}{20}\)
= \(\frac{3}{2}\)
= 3 : 2
(ii) Ratio of girls to the total number of students = 20 : 50
= \(\frac{20}{50}\)
= \(\frac{2}{5}\)
= 2 : 5
(iii) Ratio of boys to the total no of students = 30 : 50
= \(\frac{30}{50}\)
= \(\frac{3}{5}\)
= 3 : 5
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1
Objective Type Questions

Answer:

Total no of students = 50
No of boys = 30
No of girls = 50 – 30 = 20
(i) Ratio of boys to girls = 30 : 20
= \(\frac{30}{20}\)
= \(\frac{3}{2}\)
= 3 : 2
(ii) Ratio of girls to the total number of students = 20 : 50
= \(\frac{20}{50}\)
= \(\frac{2}{5}\)
= 2 : 5
(iii) Ratio of boys to the total no of students = 30 : 50
= \(\frac{30}{50}\)
= \(\frac{3}{5}\)
= 3 : 5
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1
Objective Type Questions

Q.7The ratio of ₹ 1 to 20 paise is _____v

A. 1 : 5
B. 1 : 2
C. 2 : 1
D. 5 : 1

Solution

(d) 5 : 1
Hint: ₹ 1 = 100 paise

Answer:

(d) 5 : 1
Hint: ₹ 1 = 100 paise

Q.8The ratio of 1 m to 50 cm isv

A. 1 : 50
B. 50 : 1
C. 2 : 1
D. 1 : 2

Solution

(c) 2 : 1
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Answer:

(c) 2 : 1
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Q.9The length and breadth of a window are 1 m and 70 cm respectively. The ratio of the length to the breadth isv

A. 1 : 7
B. 7 : 1
C. 7 : 10
D. 10 : 7

Solution

(d) 10 : 7

Answer:

(d) 10 : 7

Q.10The ratio of the number of sides of a triangle to the number of sides of a rectangle isv

A. 4 : 3
B. 3 : 4
C. 3 : 5
D. 3 : 2

Solution

(b) 3 : 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Answer:

(b) 3 : 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.1

Q.11If Azhagan is 50 years old and his son is 10 years old then the simplest ratio between the age of Azhagan to his son isv

A. 10 : 50
B. 50 : 10
C. 5 : 1
D. 1 : 5

Solution

(c) 5 : 1
Posted in Class 6 on January 17, 2025 January 18, 2025
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Answer:

(c) 5 : 1
Posted in Class 6 on January 17, 2025 January 18, 2025
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Q.1Fill in the blanks of the given equivalent ratios. (i) 3 : 5 = 9 : …… (ii) 4 : 5 = …… : 10 (iii) 6 : …… = 1 : 2v

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

Answer:

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

Q.3Say 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 24v

Solution

(i) False
Hint: \(\frac{21}{15}=\frac{7}{5}=7: 5\)
(ii) True
Hint: \(\frac{3}{5} \times 40=24\)
Handy LCM of two or more numbers Calculator displays LCM of 365, 838 , 862 in a fraction of seconds i.e.

Answer:

(i) False
Hint: \(\frac{21}{15}=\frac{7}{5}=7: 5\)
(ii) True
Hint: \(\frac{3}{5} \times 40=24\)
Handy LCM of two or more numbers Calculator displays LCM of 365, 838 , 862 in a fraction of seconds i.e.

Q.4Give two equivalent ratios for each of the following. (i) 3 : 2 (ii) 1 : 6 (iii) 5 : 4v

Solution

(i) 3 : 2
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2 2
3 : 2 = 6 : 4 = 9 : 6
(ii) 1 : 6

1 : 6 = 2 : 12 = 3 : 18
(iii) 5 : 4

5 : 4 = 10 : 8 = 15 : 12

Answer:

(i) 3 : 2
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2 2
3 : 2 = 6 : 4 = 9 : 6
(ii) 1 : 6

1 : 6 = 2 : 12 = 3 : 18
(iii) 5 : 4

5 : 4 = 10 : 8 = 15 : 12

Q.5Which of the two ratios is larger? (i) 4 : 5 or 8 : 15 (ii) 3 : 4 or 7 : 8 (iii) 1 : 2 or 2 : 1v

Solution

(i) 4 : 5 (or) 8 : 15
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2 5
4 : 5 > 8 : 15
(ii) 3 : 4 (or) 7 : 8

7 : 8 > 3 : 4
(iii) 1 : 2 (or) 2 : 1
1 : 2 = \(\frac{1}{2}\)
2 : 1 = \(\frac{2}{1}\)
= 2
\(\frac{2}{1}\) > \(\frac{1}{2}\)
2 : 1 > 1 : 2

Answer:

(i) 4 : 5 (or) 8 : 15
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2 5
4 : 5 > 8 : 15
(ii) 3 : 4 (or) 7 : 8

7 : 8 > 3 : 4
(iii) 1 : 2 (or) 2 : 1
1 : 2 = \(\frac{1}{2}\)
2 : 1 = \(\frac{2}{1}\)
= 2
\(\frac{2}{1}\) > \(\frac{1}{2}\)
2 : 1 > 1 : 2

Q.6Divide 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.v

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.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Answer:

(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.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Q.7In a family, the amount spent in a month for buying Provisions and Vegetables are in the ratio 3 : 2. If the allotted amount is Rs 4000, then what will be the amount spent for (i) Provisions and (ii) Vegetables?v

Solution

Allotted amount = Rs 4000
Ratio = 3 : 2
Sum of the ratio = 3 + 2 = 5
5 parts = Rs 4000
1 part = Rs \(\frac{4000}{5}\) = Rs 800
Provisions : Vegetables = 3 : 2
3 parts = 3 × Rs 800 = Rs 2400
2 parts = 2 × Rs 800 = Rs 1600
Amount spent for provisions = Rs 2400
Amount spent for vegetables = Rs 1600
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Answer:

Allotted amount = Rs 4000
Ratio = 3 : 2
Sum of the ratio = 3 + 2 = 5
5 parts = Rs 4000
1 part = Rs \(\frac{4000}{5}\) = Rs 800
Provisions : Vegetables = 3 : 2
3 parts = 3 × Rs 800 = Rs 2400
2 parts = 2 × Rs 800 = Rs 1600
Amount spent for provisions = Rs 2400
Amount spent for vegetables = Rs 1600
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Q.8A line segment 63 cm long is to be divided into two parts in the ratio 3 : 4. Find the length of each part.v

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

Answer:

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

Q.9If 2 : 3 and 4 : …… are equivalent ratios, then the missing term isv

A. 6
B. 2
C. 4
D. 3

Solution

(a) 6
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Answer:

(a) 6
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Q.10An equivalent ratio of 4 : 7 isv

A. 1 : 3
B. 8 : 15
C. 14 : 8
D. 12 : 21

Solution

(d) 12 : 21

Answer:

(d) 12 : 21

Q.11Which is not an equivalent ratio of \(\frac{16}{24}\)?v

A. \(\frac{6}{9}\)
B. \(\frac{12}{18}\)
C. \(\frac{10}{15}\)
D. \(\frac{20}{28}\)

Solution

(d) \(\frac{20}{28}\)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Answer:

(d) \(\frac{20}{28}\)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.2

Q.12If Rs 1600 is dividedv

A. Rs 480
B. Rs 800
C. Rs 1000
D. Rs 200

Solution

(c) Rs 1000
Posted in Class 6 on January 5, 2025 January 6, 2025
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Answer:

(c) Rs 1000
Posted in Class 6 on January 5, 2025 January 6, 2025
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Q.1Fill in the blanks. (i) 3 : 5 :: …….. : 20 (ii) ……… : 24 :: 3 : 8 (iii) 5 : …….. :: 10 : 8 :: 15 : ……… (iv) 12 : ……… :: ………. :: 4 = 8 : 16v

Solution

(i) 12
Hint:
5x = 3 × 20 ⇒ x = 12
(ii) 9
8x = 24 × 3 ⇒ x = 9
(iii) 4, 12
Hint:
10x = 8 × 5 = 40 ⇒ x = 4
10y = 8 × 15 = 120 ⇒ y = 12
(iv) 24, 2
Hint:
16y = 8 × 4 ⇒ y = 2
12 × 4 = 2x ⇒ x = 24
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Answer:

(i) 12
Hint:
5x = 3 × 20 ⇒ x = 12
(ii) 9
8x = 24 × 3 ⇒ x = 9
(iii) 4, 12
Hint:
10x = 8 × 5 = 40 ⇒ x = 4
10y = 8 × 15 = 120 ⇒ y = 12
(iv) 24, 2
Hint:
16y = 8 × 4 ⇒ y = 2
12 × 4 = 2x ⇒ x = 24
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Q.2Say True or False. (i) 2 : 7 : : 14 : 4 (ii) 7 Persons are to 49 Persons as 11 kg is to 88 kg (iii) 10 books are to 15 books as 3 books are to 15 books.v

Solution

(i) False
Hint:
7 × 14 ≠ 4 × 2
98 ≠ 8
(ii) False
Hint:
7 : 49 :: 11 : 48
49 × 11 ≠ 7 × 48
539 ≠ 336
(iii) False
Hint:
10 : 15 :: 3 : 5
\(\frac{10}{15}=\frac{5 \times 2}{5 \times 3}=\frac{2}{3} \Rightarrow \frac{3}{5}=\frac{3}{5}\)

Answer:

(i) False
Hint:
7 × 14 ≠ 4 × 2
98 ≠ 8
(ii) False
Hint:
7 : 49 :: 11 : 48
49 × 11 ≠ 7 × 48
539 ≠ 336
(iii) False
Hint:
10 : 15 :: 3 : 5
\(\frac{10}{15}=\frac{5 \times 2}{5 \times 3}=\frac{2}{3} \Rightarrow \frac{3}{5}=\frac{3}{5}\)

Q.3Using the numbers 3, 9, 4, 12 write two ratios that are in proportion.v

Solution

(i) 3, 9, 4, 12
Here product of extremes = 3 × 12 = 36
Product of means = 9 × 4 = 36
3 : 9 : : 4 : 12
(ii) Also if we take 9, 3, 12, 4
Product of extremes = 9 × 4 = 36
Product of means = 3 × 12 = 36
9 : 3 : : 12 : 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Answer:

(i) 3, 9, 4, 12
Here product of extremes = 3 × 12 = 36
Product of means = 9 × 4 = 36
3 : 9 : : 4 : 12
(ii) Also if we take 9, 3, 12, 4
Product of extremes = 9 × 4 = 36
Product of means = 3 × 12 = 36
9 : 3 : : 12 : 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Q.4Find whether 12, 24,18, 36 are in order that can be expressed as two ratios that are in proportion.v

Solution

Yes, 12 : 24 : : 18 : 36
Because product of extremes 12 × 36 = 432
Product of means = 24 × 18 = 432
12 : 24 :: 18 : 36.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Answer:

Yes, 12 : 24 : : 18 : 36
Because product of extremes 12 × 36 = 432
Product of means = 24 × 18 = 432
12 : 24 :: 18 : 36.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Q.5Write the mean and extreme terms in the following ratios and check whether they are in proportion. (i) 78 liters is to 130 liters and 12 bottles are to 20 bottles (ii) 400 gm is to 50 gm and 25 rupees is to 625 rupeesv

Solution

(i) 78 : 130 :: 12 : 20
Extreme terms are 78 and 20.
Mean terms are 130 and 12.
Product of Extremes = 78 × 20 = 1560
Product of Means = 130 × 12 = 1560
Product of Extremes = Product of means
It is in proportion.
(ii) 400 : 50 : : 25 : 625
Product of extremes = 400 × 625 = 2,50,000
Product of means = 50 × 25 = 1250
Here product of extremes ≠ product of means
400 : 50 and 25 : 625 are not in proportion.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Answer:

(i) 78 : 130 :: 12 : 20
Extreme terms are 78 and 20.
Mean terms are 130 and 12.
Product of Extremes = 78 × 20 = 1560
Product of Means = 130 × 12 = 1560
Product of Extremes = Product of means
It is in proportion.
(ii) 400 : 50 : : 25 : 625
Product of extremes = 400 × 625 = 2,50,000
Product of means = 50 × 25 = 1250
Here product of extremes ≠ product of means
400 : 50 and 25 : 625 are not in proportion.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Q.6America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model in proportion to the original bridge? Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3 1

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3 1

v

Solution

6480 : 756, 60 : 7
Product of the means = 756 × 60 = 45360
Product of the extremes = 6480 × 7 = 45360
ad = bc
∴ They are in proportion
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3
Objective Type Questions

Answer:

6480 : 756, 60 : 7
Product of the means = 756 × 60 = 45360
Product of the extremes = 6480 × 7 = 45360
ad = bc
∴ They are in proportion
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3
Objective Type Questions

Q.7Which of the following ratios are in proportion?v

A. 3 : 5, 6 : 11
B. 2 : 3, 9 : 6
C. 2 : 5, 10 : 25
D. 3 : 1, 1 : 3

Solution

(c) 2 : 5, 10 : 25
Hint:
2 × 25 = 5 × 10
⇒ 50 = 50

Answer:

(c) 2 : 5, 10 : 25
Hint:
2 × 25 = 5 × 10
⇒ 50 = 50

Q.8If the ratios formed using the numbers 2, 5, x, 20 in the same order are in proportion, then ‘x’ isv

A. 50
B. 4
C. 10
D. 8

Solution

(d) 8
5x = 2 × 20 ⇒ x = 8
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Answer:

(d) 8
5x = 2 × 20 ⇒ x = 8
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.3

Q.9If 7 : 5 is in proportion to x : 25, then ‘x’ isv

A. 27
B. 49
C. 35
D. 14

Solution

(c) 35
Hint:
5x = 7 × 25 ⇒ x = 35
Posted in Class 6 on January 17, 2025 January 18, 2025
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Answer:

(c) 35
Hint:
5x = 7 × 25 ⇒ x = 35
Posted in Class 6 on January 17, 2025 January 18, 2025
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Q.1Fill in the blanks. (i) If the cost of 3 pens is Rs 18, then the cost of 5 pens is …….. (ii) If Karkuzhali earns Rs 1800 in 15 days, then she earns Rs 3000 in …….. daysv

Solution

(i) ₹ 30
Hint: \(5 \times \frac{18}{3}\) = 5 × 6 = ₹ 30
(ii) 25 Days
Hint:
\(\frac{1800}{3000}=\frac{15}{x}\)
⇒ x = \(\frac{15 \times 3000}{1800}\) = 25 days

Answer:

(i) ₹ 30
Hint: \(5 \times \frac{18}{3}\) = 5 × 6 = ₹ 30
(ii) 25 Days
Hint:
\(\frac{1800}{3000}=\frac{15}{x}\)
⇒ x = \(\frac{15 \times 3000}{1800}\) = 25 days

Q.2Say True or False. (i) If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg. (ii) A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed.v

Solution

(i) True
Hint: Weight of 1 book = \(\frac{8}{40}=\frac{1}{5} \mathrm{kg}\)
Flence Weight of 15 books = \(\frac{1}{5} \times 15=3 \mathrm{kg}\)
(ii) False
1 hour the car travels = \(\frac{90}{3}\) = 30 km
In 5 hours the car travels = 30 × 5 = 150 km
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.4

Answer:

(i) True
Hint: Weight of 1 book = \(\frac{8}{40}=\frac{1}{5} \mathrm{kg}\)
Flence Weight of 15 books = \(\frac{1}{5} \times 15=3 \mathrm{kg}\)
(ii) False
1 hour the car travels = \(\frac{90}{3}\) = 30 km
In 5 hours the car travels = 30 × 5 = 150 km
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.4

Q.3If a person reads 20 pages of a book in 2 hours, how many pages will he read in 8 hours at the same speed?v

Solution

In 2 hours, pages read = 20
In 1 hour, pages read = \(\frac{20}{2}\) = 10
In 8 hours, pages read = 10 × 8
= 80 pages

Answer:

In 2 hours, pages read = 20
In 1 hour, pages read = \(\frac{20}{2}\) = 10
In 8 hours, pages read = 10 × 8
= 80 pages

Q.6Cholan walks 6 km in 1 hour at a constant speed. Find the distance covered by him in 20 minutes at the same speed.v

Solution

In 1 hour (60 minutes), distance covered = 6 km
In 1 minute, distance covered = \(\frac{6 km}{60 min}\) = \(\frac{6000 m}{60}\) = 100 m
In 20 minutes, distance covered = 20 × 100 m = 2000 m = 2 km

Answer:

In 1 hour (60 minutes), distance covered = 6 km
In 1 minute, distance covered = \(\frac{6 km}{60 min}\) = \(\frac{6000 m}{60}\) = 100 m
In 20 minutes, distance covered = 20 × 100 m = 2000 m = 2 km

Q.7The number of correct answers given by Kaarmugilan and Kavitha in a quiz competition are in the ratio 10 : 11. If they had scored a total of 84 points in the competition, then how many points did Kavitha get?v

Solution

Total points scored = 84 Ratio = 10 : 11
Sum of the ratio = 10 + 11 = 21
21 parts = 84 points
1 part = \(\frac{84}{21}\) = 4 points
Kavitha = 11 parts
Kaarmugilan = 10 parts
Foints scored by Kavitha = 11 parts = 11 × 4 points = 44 points
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.4

Answer:

Total points scored = 84 Ratio = 10 : 11
Sum of the ratio = 10 + 11 = 21
21 parts = 84 points
1 part = \(\frac{84}{21}\) = 4 points
Kavitha = 11 parts
Kaarmugilan = 10 parts
Foints scored by Kavitha = 11 parts = 11 × 4 points = 44 points
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.4

Q.8Karmegam made 54 runs in 9 overs and Asif made 77 runs in 11 overs. Whose run rate is better? (run rate = ratio of runs to overs)v

Solution

Karmegam Runs made in 9 overs = 54
Runs made in 1 over = \(\frac{54}{9}\) = 6 runs
Asif Runs made in 11 overs = 77
Runs made in 1 over = \(\frac{77}{11}\) = 7 runs
∴ Asif’s run rate is better than Karmegam.

Answer:

Karmegam Runs made in 9 overs = 54
Runs made in 1 over = \(\frac{54}{9}\) = 6 runs
Asif Runs made in 11 overs = 77
Runs made in 1 over = \(\frac{77}{11}\) = 7 runs
∴ Asif’s run rate is better than Karmegam.

Q.9You purchase 6 apples for Rs 90 and your friend purchases 5 apples for Rs 70. Whose purchase is better?v

Solution

Myself
Cost of 6 apples = Rs 90
Cost of 1 apple = \(\frac{Rs 90}{6}\) = Rs 15
Friend’s purchase
Cost of 5 apples = Rs 70
Cost of 1 apple = \(\frac{70}{5}\) = Rs 14
∴ Friend’s purchase is better than mine.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.4
Objective Type Questions

Answer:

Myself
Cost of 6 apples = Rs 90
Cost of 1 apple = \(\frac{Rs 90}{6}\) = Rs 15
Friend’s purchase
Cost of 5 apples = Rs 70
Cost of 1 apple = \(\frac{70}{5}\) = Rs 14
∴ Friend’s purchase is better than mine.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.4
Objective Type Questions

Q.10If a Barbie doll costs ₹ 90, then the cost of 3 such dolls is ₹ _____v

A. 260
B. 270
C. 30
D. 93

Solution

(b) 270
Hint:
Cost of 3 dolls = 90 × 3 = ₹ 270

Answer:

(b) 270
Hint:
Cost of 3 dolls = 90 × 3 = ₹ 270

Q.12If a man walks 2 km in 15 minutes, then he will walk _____ km in 45 minutes.v

A. 10
B. 8
C. 6
D. 12

Solution

(c) 6
Hint:
1 min he walks = \(\frac{2}{15}\) km
45 min he walks = \(\frac{2}{15}\) × 45 = 6 km.
Posted in Class 6 on January 19, 2025 January 20, 2025
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Answer:

(c) 6
Hint:
1 min he walks = \(\frac{2}{15}\) km
45 min he walks = \(\frac{2}{15}\) × 45 = 6 km.
Posted in Class 6 on January 19, 2025 January 20, 2025
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Q.1The maximum speed of some of the animals are given below: the Elephant = 20 km/h; the Lion = 80 km/h; the Cheetah =100 km/h Find the following ratios of their speeds in simplified form and find which ratio is the least? (i) the Elephant and the Lion (ii) the Lion and the Cheetah (iii) the Elephant and the Cheetahv

Solution

(i) The Elephant: the Lion
= 20 : 80 = \(\frac{20}{80}\) = \(\frac{1}{4}\) = 1 : 4
(ii) the Lion : the Cheetah
= 80 : 100 = \(\frac{80}{100}\) = \(\frac{4}{5}\) = 4 : 5
(iii) the Elephant: the Cheetah
= 20 : 100 = \(\frac{20}{100}\) = \(\frac{1}{5}\) = 1 : 5
The ratio of Elephant to Cheetah is the least.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

(i) The Elephant: the Lion
= 20 : 80 = \(\frac{20}{80}\) = \(\frac{1}{4}\) = 1 : 4
(ii) the Lion : the Cheetah
= 80 : 100 = \(\frac{80}{100}\) = \(\frac{4}{5}\) = 4 : 5
(iii) the Elephant: the Cheetah
= 20 : 100 = \(\frac{20}{100}\) = \(\frac{1}{5}\) = 1 : 5
The ratio of Elephant to Cheetah is the least.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.2A particular high school has 1500 students 50 teachers and 5 administrators. If the school grows to 1800 students and the ratios are maintained, then find the number of teachers and administrators.v

Solution

Administrators : teachers : students = 5 : 50 : 1500 = 1 : 10 : 300
If the school grows to 1800 students then 10 parts = teachers
1 part = administrators
300 parts = 1800
1 part = \(\frac{1800}{300}\) = 6
10 parts = 6 × 10 = 60
So, if the school grows to 1800 students the new ratio is administrators : teachers: students
6 : 60 : 1800
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

Administrators : teachers : students = 5 : 50 : 1500 = 1 : 10 : 300
If the school grows to 1800 students then 10 parts = teachers
1 part = administrators
300 parts = 1800
1 part = \(\frac{1800}{300}\) = 6
10 parts = 6 × 10 = 60
So, if the school grows to 1800 students the new ratio is administrators : teachers: students
6 : 60 : 1800
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.3I have a box which has 3 green, 9 blue, 4 yellow, 8 orange coloured cubes in it.v

A. What is the ratio of orange to yellow cubes?
B. What is the ratio of green to blue cubes?
C. How many different ratios can be formed, when you compare each colour to any one of the other colours?

Solution

Number of green cubes = 3
Number of blue cubes = 9
Number of yellow cubes = 4
Number of orange cubes = 8
(a) Ratio of orange to yellow cubes \(\frac{\text { Number of orange cubes }}{\text { Number of yellow cubes }}=\frac{8}{4}=\frac{2}{1}=2: 1\)
Ratio of orange to yellow cubes = 2 : 1
(b) \(\frac{\text { Number of green cubes }}{\text { Number of blue cubes }}=\frac{3}{9}=\frac{1}{3}\)
Ratio of green to blue cubes = 1 : 3
(c) The ratios can be Orange : Yellow, Orange: blue, Orange : green, Yellow : Orange, yellow : blue, yellow : green, blue : green, blue : orange, blue : yellow, green : orange, green : yellow, green : blue. Thus 12 ratios can be formed.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

Number of green cubes = 3
Number of blue cubes = 9
Number of yellow cubes = 4
Number of orange cubes = 8
(a) Ratio of orange to yellow cubes \(\frac{\text { Number of orange cubes }}{\text { Number of yellow cubes }}=\frac{8}{4}=\frac{2}{1}=2: 1\)
Ratio of orange to yellow cubes = 2 : 1
(b) \(\frac{\text { Number of green cubes }}{\text { Number of blue cubes }}=\frac{3}{9}=\frac{1}{3}\)
Ratio of green to blue cubes = 1 : 3
(c) The ratios can be Orange : Yellow, Orange: blue, Orange : green, Yellow : Orange, yellow : blue, yellow : green, blue : green, blue : orange, blue : yellow, green : orange, green : yellow, green : blue. Thus 12 ratios can be formed.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.4A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not.v

Solution

Let x be the part owned by C then A : B : C = 2(2x) : 2x : x = 4x : 2x : x
A : B = 4x : 2x = 2 : 1
B : C = 2x : x = 2 : 1
A : B : : B : C. i.e, They are in proportion.

Answer:

Let x be the part owned by C then A : B : C = 2(2x) : 2x : x = 4x : 2x : x
A : B = 4x : 2x = 2 : 1
B : C = 2x : x = 2 : 1
A : B : : B : C. i.e, They are in proportion.

Q.5The ingredients required for the preparation of Ragi Kali, a healthy dish of Tamilnadu is given below. Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5 1

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5 1

v

A. If one cup of ragi flour is used then, what would be the amount of raw rice required?
B. If 16 cups of water are used, then how much ragi flour should be used?
C. Which of these ingredients cannot be expressed as a ratio? Why?

Solution

(i) \(\frac{1}{4}\) cup
(ii) 8 cups
(iii) Ragi flour, Raw rice, and water are in one unit. Sesame oil and salt are in different units. These different units cannot be compared and cannot be expressed as a ratio because the two quantities of a ratio should be in the same unit.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

(i) \(\frac{1}{4}\) cup
(ii) 8 cups
(iii) Ragi flour, Raw rice, and water are in one unit. Sesame oil and salt are in different units. These different units cannot be compared and cannot be expressed as a ratio because the two quantities of a ratio should be in the same unit.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.6Antony brushes his teeth in the morning and night on all days of the week. Shabeen brushes her teeth only in the morning. What is the ratio of the number of times they brush their teeth in a week?v

Solution

Number of times Antony brushes a day = 2
Number of times Antony brushes a week = 2 × 7 = 14
Number of times Shabeen brushes a day = 1
Number of times Shabeen brushes a week = 1 × 7 = 7
Number of times Antony brushes : Number of times Antony brushes = 14 : 7 = 2 : 1
The required ratio = 2 : 1

Answer:

Number of times Antony brushes a day = 2
Number of times Antony brushes a week = 2 × 7 = 14
Number of times Shabeen brushes a day = 1
Number of times Shabeen brushes a week = 1 × 7 = 7
Number of times Antony brushes : Number of times Antony brushes = 14 : 7 = 2 : 1
The required ratio = 2 : 1

Q.7Thirumagal’s mother wears a bracelet made of 35 red beads and 30 blue beads. Thirumagal wants to make smaller bracelets using the same two coloured beads in the same ratio. In how many different ways can she make the bracelets? Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5 2

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5 2

v

Solution

Red : blue = 35 : 30 = 7 : 6
Different ways (i) 7 : 6
(ii) 14 : 12;
(iii) 21 : 18;
(iv) 28 : 24
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

Red : blue = 35 : 30 = 7 : 6
Different ways (i) 7 : 6
(ii) 14 : 12;
(iii) 21 : 18;
(iv) 28 : 24
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.8Team A wins 26 matches out of 52 matches. Team B wins three fourth of 52 matches played. Which team has a better winning record?v

Solution

Team A = \(\frac{26}{52}\) = \(\frac{1}{2}\)
Team B = \(\frac{3}{4}\) × 52 = 39
Team B has a better winning record.

Answer:

Team A = \(\frac{26}{52}\) = \(\frac{1}{2}\)
Team B = \(\frac{3}{4}\) × 52 = 39
Team B has a better winning record.

Q.9In a school excursion, 6 teachers and 12 students from 6th standard and 9 teachers and 27 students from 7th standard, 4 teachers and 16 students from 8th standard took part. Which class has the least teacher to student ratio?v

Solution

Std VI – teachers: students = 6 : 12 = 1 : 2
Std VII – teachers : students = 9 : 27 = 1 : 3
Std VIII – teachers : students = 4 : 16 = 1 : 4
Std VIII has the least ratio.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

Std VI – teachers: students = 6 : 12 = 1 : 2
Std VII – teachers : students = 9 : 27 = 1 : 3
Std VIII – teachers : students = 4 : 16 = 1 : 4
Std VIII has the least ratio.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.10Fill the boxes using any set of suitable numbers 6 : ___ : : ___ : 15v

Solution

6 : ……. = …….. : 15
Product of the extremes = 6 × 15 = 90
Set of suitable numbers
1 and 90, 2 and 45, 3 and 30, 5 and 18, 6 and 15

Answer:

6 : ……. = …….. : 15
Product of the extremes = 6 × 15 = 90
Set of suitable numbers
1 and 90, 2 and 45, 3 and 30, 5 and 18, 6 and 15

Q.11From your school diary, write the ratio of the number of holidays to the number of working days in the current academic year.v

Solution

Number of holidays = 145
Number of working days = 220
Holidays : working days = 145 : 220
= \(\frac{145}{220}\)
= \(\frac{29}{44}\)
= 29 : 44
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Answer:

Number of holidays = 145
Number of working days = 220
Holidays : working days = 145 : 220
= \(\frac{145}{220}\)
= \(\frac{29}{44}\)
= 29 : 44
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 3 Ratio and Proportion Ex 3.5

Q.12If the ratio of Green, Yellow and Black balls in a bag is 4 : 3 : 5, thenv

A. Which is the most likely ball that you can choose from the bag?
B. How many balls in total are there in the bag if you have 40 black balls in it?
C. Find the number of green and yellow balls in the bag.

Solution

Green : Yellow : Black = 4 : 3 : 5
(i) Blackballs;
(ii) 96 balls (32 + 24 + 40);
(iii) green balls = 32
yellow balls = 24
Posted in Class 6 on January 19, 2025 January 20, 2025
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Answer:

Green : Yellow : Black = 4 : 3 : 5
(i) Blackballs;
(ii) 96 balls (32 + 24 + 40);
(iii) green balls = 32
yellow balls = 24
Posted in Class 6 on January 19, 2025 January 20, 2025
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