NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 - Exercise 7.1

Mastering the relationship between varying quantities is simple with our NCERT Solutions for Class 8 Maths Ch 7: Proportional Reasoning – Exercise 7.1. This exercise introduces the concept of Direct Proportion, where two quantities increase or decrease together such that their ratio remains constant.

Class 8 Math Lessons (Ch 7): Learn to Solve Ratio and Proportion Problems with Ease! The solutions to Exercise 7.1 will be presented in a step-by-step approach to help students understand the formula $\frac{x _{1}}{y _{1}} = \frac{x _{2}}{y _{2}}$ . These solutions follow CBSE Guidelines to help you improve speed and accuracy in real-world applications like unit conversion, mapping, and fuel consumption.

1.0Download NCERT Solutions for Class 8 Maths Chapter 7 Ex 7.1 : Free PDF

Our easy-to-follow NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1 are available for download as a PDF. Perfect for offline study and quick reference.

NCERT Solutions Class 8 Maths Chapter 7 Ex 7.1

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2.0Detailed NCERT Class 8 Maths Chapter 7 Solutions of Exercise 7.1

1.Circle the following statements of proportion that are true. (i) $4 : 7 :: 12 : 21$ (ii) $8 : 3 :: 24 : 6$ (iii) $7 : 12 :: 12 : 7$ (iv) $21 : 6 :: 35 : 10$ (v) $12 : 18 :: 28 : 12$ (vi) $24 : 8 :: 9 : 3$

Sol. (i) Given statement is $4 : 7 :: 12 : 21$ . This is true if $\frac{4}{7} = \frac{12}{21}$ Here $\frac{12}{21} = \frac{12 \div 3}{21 \div 3} = \frac{4}{7} = \frac{4}{7}$ ∴ The given statement is true. (ii) Given statement is $8 : 3 :: 24 : 6$ .

This is true if, $\frac{8}{3} = \frac{24}{6}$ Here $\frac{24}{6} = \frac{24 \div 3}{6 \div 3} = \frac{8}{2} = 4 \neq = \frac{8}{3}$ ∴ The given statement is not true. (iii) Given statement is $7 : 12 :: 12 : 7$ .

This is true if, $\frac{7}{12} = \frac{12}{7}$ Here $\frac{7}{12} \neq = \frac{12}{7}$ ∴ The given statement is not true. (iv) Given statement is $21 : 6 :: 35 : 10$ .

This is true if, $\frac{21}{6} = \frac{35}{10}$ Here $\frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2}; \frac{35}{10} = \frac{35 \div 5}{10 \div 5} = \frac{7}{2}$ ∴ The given statement is true. (v) Given statement is $12 : 18 :: 28 : 12$ .

This is true if, $\frac{12}{18} = \frac{28}{12}$ Here $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}; \frac{28}{12} = \frac{28 \div 4}{12 \div 4} = \frac{7}{3}$ and $\frac{2}{3} \neq = \frac{7}{3}$ ∴ The given statement is not true. (vi) Given statement is $24 : 8 :: 9 : 3$ .

This is true if, $\frac{24}{8} = \frac{9}{3}$ Here $\frac{24}{8} = 3; \frac{9}{3} = 3$ and $3 = 3$ $∴$ The given statement is true. 2. Give 3 ratios that are proportional to $4 : 9$ . $____$ : $____$ : $____$ : $____$

Sol. The given ratio is $4 : 9$ . We have $\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{4 \times 3}{9 \times 3} = \frac{4 \times 4}{9 \times 4}$ or $\frac{4}{9} = \frac{8}{18} = \frac{12}{27} = \frac{16}{36}$ $∴ 4 : 9 :: 8 : 18; 4 : 9 :: 12 : 27$ , and $4 : 9 :: 16 : 36$ $∴$ Ratios $8 : 18, 12 : 27$ and $16 : 36$ are proportional to the given ratio $4 : 9$ . 3. Fill in the missing numbers for these ratios that are proportional to $18 : 24$ . (i) 3 : $____$ (ii) 12 : $____$ (iii) 20 : $____$ (iv) 27 : $____$

Sol. (i) Given ratio is $18 : 24$ . Let $18 : 24 :: 3 : x$ $∴ \frac{18}{24} = \frac{3}{x}$ or $\frac{3}{4} = \frac{3}{x}$ or $x = 4$ ∴ Missing number in the ratio 3 : $____$ is 4 . (ii) Let $18 : 24 :: 12 : x$ .

$\frac{18}{24} = \frac{12}{x} or \frac{3}{4} = \frac{12}{x} or 3 x = 48 or x = \frac{48}{3} = 16$

∴ Missing number in the ratio 12 : $____$ is 16 . (iii) Let $18 : 24 :: 20 : x$ . $∴ \frac{18}{24} = \frac{20}{x}$ or $\frac{3}{4} = \frac{20}{x}$ or $3 x = 80$ or $x = \frac{80}{3}$ ∴ Missing number in the ratio 20 : $____$ is $\frac{80}{3}$ . (iv) Let $18 : 24 :: 27 : x$ . $∴ \frac{18}{24} = \frac{27}{x}$ or $\frac{3}{4} = \frac{27}{x}$ or $3 x = 108$ or $x = \frac{108}{3} = 36$ ∴ Missing number in the ratio 27 : $____$ is 36 . 4. Look at the following rectangles. Which rectangles are similar to each other? You can verify this by measuring the width and height using a scale and comparing their ratios.

Sol. Using a scale, we measure the width and height of given rectangles. Here, the ratio 'Width : Height' for given rectangles $A, B, C, D$ , and E are respectively $1 : 3, 3$ : $2, 9 : 4, 7 : 2$ and $3 : 1$ .

These ratios are all distinct. The ratios of A and E are $1 : 3$ and $3 : 1$ respectively.

Rectangle	Width (in mm)	Height (in mm)	Ratio $= \frac{Width}{Height}$
A	5	15	$\frac{5}{15} = \frac{1}{3}$
B	15	10	$\frac{15}{10} = \frac{3}{2}$
C	45	20	$\frac{45}{20} = \frac{9}{4}$
D	35	10	$\frac{35}{10} = \frac{7}{2}$
E	15	5	$\frac{15}{5} = \frac{3}{1}$

∴ For A and E, one side is 3 times the other side. ∴ Only rectangles A and E are similar. 5. Look at the following rectangle. Can you draw a smaller rectangle and a bigger rectangle with the same width-to-height ratio in your notebook? Compare your rectangles with your classmates' drawings. Are all of them the same? If they are different from yours, can you think why? Are they wrong?

Sol: For the given rectangle, Width $= 32 mm$ and height $= 18 mm$ ∴ Ratio is $32 : 18$ . We shall draw smaller and bigger rectangles and similar to the given rectangle by considering different 'factors of change'. (i) Let the factor of change be $\frac{1}{2}$ ∴ New width $= \frac{1}{2} \times 32 = 16 mm$ and new height $= \frac{1}{2} \times 18 = 9 mm$ A new, similar rectangle is shown in the figure.

(ii) Let 'factor of change' be 2 . ∴

New width

= 2 \times 32 = 64 mm

and new height

= 2 \times 18 = 36 mm

A new, similar rectangle is shown in the figure. The rectangles drawn by other classmates are all different, but they are all similar to the given rectangle. 6. The following figure shows a small portion of a long brick wall with patterns made using coloured bricks. Each wall continues this pattern throughout the wall. What is the ratio of grey bricks to coloured bricks? Try to give the ratios in their simplest form. (a)

(b)

Sol. (a) We consider one set of patterns in the given wall.

Number of grey bricks in one set of pattern $= 2 + 3 + 4 = 9$ Number of coloured bricks in one set of pattern $= 3 + 2 + 1 = 6$ ∴ Ratio of grey bricks to coloured bricks $= 9 : 6$ We have $9 : 6 = 3 : 2$ $∴$ Ratio in the simplest form $= 3 : 2$ (b) We use one set of patterns on the given wall

Number of grey bricks in one set of pattern

$= (\frac{1}{2} + 1 + 1 + \frac{1}{2}) + (\frac{1}{2} + 1 + 1 + \frac{1}{2}) + (\frac{1}{2} + 1 + 1 + \frac{1}{2}) + (\frac{1}{2} + 1 + 1 + \frac{1}{2}) + [1 + 1 + 1 + 1] = (3 + 3 + 3 + 3 + 4) = 16$

Number of coloured bricks in one set of pattern

$= 1 + (1 + 1) + (1 + 1) + (1 + 1) + (1 + 1) + (1 + 1) + 1 = 1 + 2 + 2 + 2 + 2 + 2 + 1 = 12$

∴ Ratio of grey bricks to coloured bricks $= 16 : 12$ We have $16 : 12 = 4 : 3$ $∴$ Ratio in the simplest form $= 4 : 3$ 7. Let us draw some human figures. Measure your friend's body-the lengths of their head, torso, arms, and legs. Write the ratios as mentioned below.

head : torso

____

____

torso : arms

____

____

torso : legs

____

____

Sol. Head : Torso

The ratio of the length of the head to the length of the torso. For instance, if the length of the head is 10 cm and the length of the torso is 30 cm , the ratio would be: Head : Torso $= \frac{Head}{Torso} = \frac{10}{30} = \frac{1}{3}$

Torso : Arms

The ratio of the length of the torso to the length of the arms. For example, if the length of the torso is 30 cm and the length of the arms is 20 cm , the ratio would be: Torso : Arms $= \frac{Torso}{Arms} = \frac{30}{20} = \frac{3}{2}$

Torso : Legs

The ratio of the length of the torso to the length of the legs. For example, if the length of the torso is 30 cm and the length of the legs is 50 cm , the ratio would be: Torso : Legs $= \frac{Torso}{Legs} = \frac{30}{50} = \frac{3}{5}$

Multiple choice questions

1.The cost of a car is ₹5,00,000. The cost of a motorbike is $₹60, 000$ . The ratio of the cost of motorbike to the cost of car is (1) $1 : 6$ (2) $3 : 25$ (3) $1 : 4$ (4) $25 : 3$

2. The ratio of 1.5 m to 100 cm is (1) $1 : 15$ (2) $15 : 10$ (3) $10 : 15$ (4) $15 : 1$

3. In $4 : 7 :: 16 : 28, 4$ and 28 are (1) extreme terms (2) mean terms (3) 7 mean term and 16 extreme term (4) none of these

4. The value of x if $42, x, 18, 3$ are in proportion is (1) 6 (2) 54 (3) 7 (4) none of these

5. If 25,35 and $x$ are in continued proportion, then find the value of x . (1) 45 (2) 25 (3) 64 (4) 49

6. The mean proportion between 16 and 49 is (1) 7 (2) 14 (3) 28 (4) 196

7. The third proportional to 4 and 6 is (1) 1 (2) 9 (3) 16 (4) 32

8. The fourth term in the proportion 2.5, 50, 7.5 is (1) 54 (2) 540 (3) 150 (4) 0.54

9. On dividing ₹210 between A and B in the ratio 5 : 2 , the share of $A$ is (1) ₹100 (2) ₹40 (3) ₹150 (4) none of these

10. The ratio $28 : 48$ in the simplest form is (1) $5 : 7$ (2) $7 : 12$ (3) $5 : 12$ (4) none of these

11. The ratio of the number of sides of a square to the number of edges of a cube is (1) $1 : 2$ (2) $1 : 3$ (3) $3 : 1$ (4) $4 : 1$

12. There are 'b' boys and 'g' girls in a school. The ratio of girls to the total number of students in the class is (1) $\frac{b}{b + a}$ (2) $\frac{g}{b + g}$ (3) $\frac{b}{g}$ (4) $\frac{b + g}{g}$

13. Which of the following is not in proportion? (1) $25 cm : 1 m$ and ₹50: ₹200 (2) $0.9 : 0.36$ and $10 : 4$ (3) $150 g : 2 kg$ and 9 minutes : 2 hours (4) $5.2 : 3.9$ and $3 : 4$

14. Which of the following is false? (1) $25 g : 30 g :: 40 kg : 48 kg$ (2) $80 : 90 :: 24 h : 27 h$ (3) $32 m : 40 m :: 6$ minutes : 12 minutes (4) $25 km : 60 km ::$ ₹ $10 :$ ₹ 24

15. If a bus travels 200 km in 4 hours and a train travels 350 km in 5 hours at uniform speeds, then the ratio of the distance travelled by them in one hour is (1) $4 : 7$ (2) $5 : 7$ (3) $4 : 5$ (4) $7 : 5$

16. The present age of Hari Kishan is 60 years. The present age of Manish is 30 years. The ratio of the age of Manish to the age of Hari Kishan 10 years ago was (1) $2 : 5$ (2) $5 : 2$ (3) $2 : 3$ (4) $3 : 2$

17. 100 students appeared in annual examination. 60 students passed. The ratio of the number of students who failed to the total number of students is (1) $5 : 2$ (2) $2 : 5$ (3) $2 : 3$ (4) $3 : 2$

18. ₹100 are divided between Sangeeta and Manish in the ratio 4:1. Find the amount Sangeeta gets (1) ₹ 80 (2) ₹ 20 (3) ₹ 60 (4) ₹ 50

19. Statement-1: The cost of each banana, when 1 dozen bananas cost ₹30, is ₹2.50. Statement-2: If 6 oranges cost ₹18, then the ratio of the cost of a banana to the cost of an orange is $5 : 6$ . (1) Statement-1 is true and Statement-2 is false. (2) Statement-1 is false and Statement-2 is true. (3) Both the statements are true. (4) Both the statements are false.

20. Statement-1: In a society, the number of males and females are 50 and 40 respectively so the ratio of the males to the females in a society is $5 : 4$ . Statement-2: The total number of persons in the society must be a multiple of 9 . (1) Statement-1 is true and Statement-2 is false. (2) Statement-1 is false and Statement-2 is true. (3) Both the statements are true. (4) Both the statements are false.

True or False

21.The ratio of 200 cm to 2 cm is $100 : 1$ .

22. If four quantities are in proportion, then the product of the first two is equal to the product of the last two.

23. $2 km : 25 km = ₹5$ : ₹ 62.5 .

24. A ratio is always more than 1 .

Fill in the blanks

Two quantities can be compared only if they are in the same $____$ . PR01-1576
$a, b, c$ are said to be in $____$ proportion if $a : b = b : c$ .

27. The first term of a ratio is called $____$ and the second term is called $____$ 。

28. In a statement of proportion, the first and fourth terms are known as $____$ while second and third terms are known as $____$ terms.

Match the column

Column - I		Column - II
(1)	₹ 60 : ₹ 150	(a)	1000:1
(2)	$50 cm : 5 m$	(b)	1:4
(3)	$60 kg : 60 g$	(c)	45:135
(4)	$15 hrs : 40 hrs$	(d)	2:5
(5)	6.25 : 25	(e)	24:56
(6)	15 : 45	(f)	3:8
(7)	30: 70	(g)	1:11
(8)	50 paise : ₹ 5.50	(h)	1 : 10

Crossword puzzle 30. Solve the following crossword puzzle, hints are given below :

Across

The method in which we first find the value of one unit from the given quantities and then the required quantity.
The name of symbol ':'
3 in the ratio $5 : 3$ .

Down

9, 15 and 25 are in $____$ proportion.
The name of symbol ': :'.
6 in the ratio $6 : 11$ .
$10 : 3$ is $____$ form of ratio 50 : 15 .

ANSWER KEY

Multiple Choice Questions

Question	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Answer	$2$	$2$	$1$	$3$	$4$	$3$	$2$	$3$	$3$	$2$	$2$	$2$	$4$	$3$	$2$
Question	16	17	18	19	20
Answer	$1$	$2$	$1$	$3$	$3$

True or False

True
False
False
False

Fill in the blanks 25. Unit 26. Continued 27. Antecedent, consequent 28. Extremes, mean

Match the column 29. (1) → (d); (2) $\to (h); (3) \to (a); (4) \to (f); (5) \to (b); (6) \to (c); (7) \to (e); (8) \to (g)$

3.0Crossword puzzle

4.0Key Concepts of Chapter 7 Proportional Reasoning 1 Exercise 7.1

Understanding Direct Proportion: Two quantities x and y are in direct proportion if they increase or decrease together in such a way that $\frac{x}{y}$ remains constant (k).
The Constant of Variation (k): The fixed ratio between two proportional quantities.
Unitary Method vs. Proportion Method: While the unitary method finds the value of one unit, the proportion method uses the cross-multiplication of ratios.
Real-world Examples:
The more kilometers a car travels, the more petrol it consumes.
The more hours you work at a fixed rate, the more salary you earn.

5.0NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 : All Exercises

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 - Exercise 7.1

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 - Exercise 7.2

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 - Exercise 7.3

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 - Exercise 7.4

6.0Benefits of NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1

Conceptual Clarity: Clearly explains how to identify if two variables are moving in the same direction.
Calculation Speed: Teaches simplification techniques before multiplication to handle large numbers.
Exam-Oriented: Focuses on conversion errors (like km/h to m/s) which are common in tests.