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

Mastering the logic of opposite variations is simple with our NCERT Solutions for Class 8 Maths Ch 7: Proportional Reasoning – Exercise 7.2. In this exercise, we move from direct relationships to Inverse Proportion. This occurs when an increase in one quantity leads to a proportional decrease in the other, and vice versa.

Class 8 Math Lessons (Ch 7): Learn to Solve Inverse Variation Problems with Ease! The solutions to Exercise 7.2 will be presented in a step-by-step approach to help students apply the formula $x_{1} y_{1} = x_{2} y_{2}$ . These solutions follow CBSE Guidelines to help you master problems related to work-time efficiency, speed-time relationships, and sharing resources among varying numbers of people.

1.0Download NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 Ex 7.2 : Free PDF

Our easy-to-follow NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 are available for download as a PDF. Perfect for offline study and quick reference.

NCERT Solutions Class 8 Maths Chapter 7 Ex 7.2

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2.0Detailed NCERT Class 8 Maths Chapter 7 Solutions of Exercise 7.2

1.The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week? Sol. We know that: 1 million = 10 lakh = 10,00,000 and 1 year $= \frac{365}{7}$ weeks 940 million kilometres, i.e., $940 \times 10, 00, 000$ kilometres, are travelled by the Earth in 1 year, i.e., in $\frac{365}{7}$ weeks. Let the Earth travel x kilometres 1 week ∴ The ratios $940 \times 10, 00, 000 : \frac{365}{7}$ and $x : 1$ are in proportion. $\Rightarrow \frac{940 \times 1000000}{\frac{365}{7}} = \frac{x}{1}$ $\Rightarrow x = \frac{940 \times 1000000 \times 7}{365}$ $\Rightarrow x = \frac{188 \times 7000000}{73}$ $\Rightarrow x = 18027397$ (nearly) ∴ In week, Earth travels nearly $1, 80, 27, 397$ kilometres around the Sun.

2.A mason is building a house in the shape shown in the diagram. He needs to construct both the outer walls and the inner wall that separates the two rooms. To build a wall of 10 feet, he requires approximately 1450 bricks. How many bricks would he need to build the house? Assume all walls are of the same height and thickness.

Sol.

Number of bricks required for a 10 ft wall $= 1450$ ∴ Ratio of length of wall to number of bricks $= 10 : 1450$ Total length of walls $= AI + CH + DE + FG + IG + AF + CD$ $= 12 + (9 + 12) + 9 + 12 + (9 + 15) + (9 + 15) + 6 = 108 ft$ Let x bricks be required for a 108 ft long wall. ∴ Ratio of length of wall to number of bricks $= 108 : x$ These ratios are in proportion. $∴ 10 : 1450 :: 108 : x$ $\Rightarrow \frac{10}{1450} = \frac{108}{x}$ $\Rightarrow \frac{1}{145} = \frac{108}{x}$ $\Rightarrow x = 145 \times 108 = 15, 660$ $∴$ Number of required bricks

Very short answer type questions

1.Find each of the following ratios in the simplest form: (i) 24 to 56 (ii) 84 paise to ₹ 3 (iii) 4 kg to 750 gm (iv) 1.8 kg to 6 kg (v) 48 minutes to 1 hour (vi) 24 km to 9 km

2. Mr. Sahai and his wife are both schoolteachers and earn ₹16800 and ₹10500 per month respectively. Find the ratio of (i) Mr. Sahai's income to his wife's income. (ii) Mrs. Sahai's income to her husband's income. (iii) Mr. Sahai's income to the total income of the two.

3. A tempo travels 60 km in 2 hour and a car travels 80 km in 1 hour. Find the ratio of their speed.

4. Determine whether the following ratios form a proportion or not. (i) $1 L : 250 mL$ and ₹1000: ₹500 (ii) ₹2000 : ₹200 and 100 bottles : 50 bottles

3.0Short answer type questions

5.In class VI of a school having 50 students, 20 play cricket, 10 play table tennis and 15 play badminton. The remaining students do not play any game. No student is allowed to play more than one game. Find the ratio of the number of students (i) Playing cricket to the number who play table tennis. (ii) Playing table tennis to the number who play badminton. (iii) Playing some game to the number who do not play any game. (iv) Playing some game to the total number of students.

6. A company manufactures three types of electronic components, $A, B$ , and C . The ratio of the number of components produced is $5 : 7 : 9$ , respectively. (i) Production Adjustment: Due to a sudden increase in demand, the company decides to increase the production of each component by $20%$ . How will the new production ratio of the components compare to the old one? Provide the new ratio in its simplest form. (ii) Workforce Proportions: The total workforce is divided between the three components in the same ratio as their production. If the company employs a total of 1,000 workers, how many workers are assigned to produce each component ( $A, B$ , and C )? (iii) Profit Distribution: The profit earned from selling the components is directly proportional to the number of components produced. If the company earns a total profit of ₹5,40,000 from selling all three types of components, how much profit is generated from the sale of each type?

7. Present age of Ashima is 16 years and that of her mother is 32 years. Find the ratio of (i) Present age of mother to the present age of Ashima. (ii) Age of the mother to the age of Ashima, when Ashima was 10 years old. (iii) Age of Ashima after 8 years to the age of her mother after 8 years.

8. Divide ₹ 1800 among three persons in the ratio 1 : 4 : 5 .

9. Anant covers a distance of 225 km in 5 hours in his car. How much distance will he be able to cover in 7 hours? Find the answer using proportions.

10. An electric pole casts a shadow of length 18 m at a time when a tree 12 m high casts a shadow 9 m long. Find the height of the pole.

11. The sides of a triangle are in the ratio $1 : 2 : 3$ . If the perimeter is 36 cm , find its sides.

12. Salaries of Ravi and Sumit are in the ratio $2 : 3$ . If the salary of each is increased by Rs. 4000, the new ratio becomes $40 : 57$ . What is Sumit's salary?

13. Find mean proportion between (i) 12 and 3 (ii) 50 and 8 (iii) 27 and 48 (iv) 50 and 98 14. If Rs. 782 be divided into three parts, proportional to $\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$ , then find first part.

15. If $x : y = 8 : 9$ , find the ratio $(7 x - 4 y)$ : $(3 x + 2 y)$ .

16. Find the ratio of the price of pencil to that of ball pen, if pencil cost Rs. 16 per score and ball pen cost Rs.8.40 per dozen.

17. Two liquids A and B are mixed in ratio 3:5. How much of each is needed to make 64 L mixture?

18. A invests $20, 000, B$ invests ₹ 30,000 , and C invests ₹50,000. A withdraws after 6 months, B after 9 months. Find ratio of profits after 1 year.

19. Alice, Bob, and Charlie have candies in the ratio $2 : 3 : 5$ . Charlie gives 10 candies to Alice, and now the ratio of Alice to Charlie becomes 1: 2. How many candies did they have initially?

Long answer type questions

20.A box contains candies for three friends $A, B$ , and C in the ratio $3 : 4 : 5$ . (i) If the total number of candies is 120 , how many candies does each get? (ii) A eats 6 candies B gives 4 candies to C. Find the new ratio. (iii) If they share the remaining candies equally, how many candies will each get? (iv) What fraction of the total candies did A finally get?

21. A school collects money from three classes in the ratio $4 : 5 : 6$ . (i) If the total fund is ₹15,000, find the contribution of each class. (ii) Class-1 spends ₹1,200, class-2 spends ₹1,500, class-3 spends ₹2,000. How much is left with each class? (iii) Find the new ratio of remaining money. (iv) How much more money does class-3 have than class-1 after spending?

22. Father and son's ages are in ratio $7 : 3$ . (i) If father is 42 , find son's age. (ii) After 6 years, find the new ratio of their ages. (iii) How many years ago was the father 5 times as old as son? (iv) Find the difference in their ages.

23. A ribbon is divided into 3 parts in ratio $2 : 3 : 4$ . (i) If the ribbon is 36 meters long, find the length of each part. (ii) If the first part is shortened by 2 meters and the second part increased by 2 meters, find the new lengths. (iii) Find the new ratio. (iv) What is the difference between the longest and shortest part now?

24. A fruit basket contains apples, oranges, and bananas in the ratio $3 : 4 : 5$ . (i) If there are 60 fruits in total, how many of each fruit? (ii) 6 apples and 8 oranges are taken out. How many of each fruit remain? (iii) Find the new ratio of remaining fruits. (iv) If 5 more bananas are added, what is the new ratio?

25. (i) Find the mean proportion between 4 and 9. (ii) Find the third proportional to 12 and 30.

PR06-0109

ANSWER KEY

4.0Very short answer type questions

1.(i) $3 : 7$ (ii) $7 : 5$ (iii) $16 : 3$ (iv) $3 : 10$ (v) $4 : 5$ (vi) $8 : 3$

2.(i) $8 : 5$ (ii) $5 : 8$ (iii) $8 : 13$

3.3: 8

4.(i) No (ii) No

Short answer type questions 5. (i) $2 : 1$ (ii) $2 : 3$ (iii) $9 : 1$ (iv) $9 : 10$ 6. (i) $5 : 7 : 9$ (ii) Workers are 238 for $A, 333$ for B , and 429 for C . (iii) Profit for $A =$ ₹ $1, 28, 571.43$

Profit for $B = ₹1, 80, 000$ Profit for C = ₹2,31,428.57 7. (i) $2 : 1$ (ii) $13 : 5$ (iii) $3 : 5$ 8. ₹ 180, ₹ 720, ₹ 900 9. 315 km 10. 6 m 11. $6 cm, 12 cm, 18 cm$ 12. Rs 38,000 13. (i) 6 (ii) 20 (iii) 36 (iv) 70 14. Rs. 204 15. $10 : 21$ 16. $8 : 7$ 17. $A = 24 L, B = 40 L$ 18. $4 : 9 : 20$ 19. Alice $= 60$ candies, $Bob = 90$ candies, Charlie $= 150$ candies

Long answer type questions 20. (i) $A = 30, B = 40, C = 50$ (ii) $4 : 6 : 9$ (iii) 38 (iv) $\frac{19}{60}$ 21. (i) Class- $1 = 4, 000$ , Class- $2 = 5, 000$ , Class- $3 = 6, 000$ (ii) Class-1 = 2,800,

Class-2 $= 3, 500$ , Class-3 $= 4, 000$ (iii) $28 : 35 : 40$ (iv) 1,200 22. (i) 18 (ii) $2 : 1$ (iii) 12 years (iv) 24 23. (i) $8, 12, 16$ (ii) $6, 14, 16$ (iii) $3 : 7 : 8$ (iv) 10 meters 24. (i) Apples $= 15$ , Oranges $= 20$ , Bananas $= 25$ (ii) Apples $= 9$ , Oranges $= 12$ , Bananas $= 25$ (iii) $9 : 12 : 25$ (iv) $3 : 4 : 10$ 25. (i) 6 (ii) 75

5.0Key Concepts of Chapter 7 Proportional Reasoning 1 Exercise 7.2

Understanding Inverse Proportion: Two quantities x and y are in inverse proportion if an increase in x causes a proportional decrease in y such that their product xy remains constant (k).
The Constant Product: Unlike direct proportion where the ratio is constant, here $x \times y = k$ .
Speed and Time: For a fixed distance, if speed increases, the time taken decreases. This is a classic example of inverse variation.
Work and People: If the amount of work is constant, increasing the number of workers will decrease the time required to finish the task.

6.0NCERT 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

7.0Benefits of NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2

Conceptual Clarity: Helps students distinguish between "more leads to more" (Direct) and "more leads to less" (Inverse).
Logical Structuring: Teaches the table method to organize data before choosing a formula.
Exam Readiness: Covers common "work-men" problems that are frequently asked in competitive exams like the SAT or Olympiads.

NCERT Class 8 Maths Ch. 7 Proportional Reasoning Other Exercises:-

Exercise 7.1