NCERT Solutions For Class 8 Maths Chapter 7 Proportional Resoning

NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning helps students understand the relationship between quantities that change in the same ratio. This chapter explains direct proportion, inverse proportion, unitary method, and real-life applications such as speed, cost, time, and work. Students learn how to compare quantities, solve ratio-based problems, and use logic in calculations. These concepts are very useful in arithmetic, algebra, and everyday problem-solving. Regular practice improves analytical thinking and numerical accuracy.

Question & Answers

Q1. What is direct proportion?

Answer: Two quantities are in direct proportion when one increases, the other also increases in the same ratio.

NCERT Solutions For Class 8 Maths Chapter 7 Proportional Resoning

Proportional Reasoning-1 (New NCERT)
Medium
Q.
(i) Are the ratios 3 : 4 and 72 : 96 proportional?
(ii) What is the HCF of 72 and 96?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Last year, we hired 3 buses for the school trip. We had a total of 162 students and teachers who went on that trip, and all the buses were full. This year we have 204 students. How many buses will we need? Will all the buses be full?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Divide ₹ 4,500 into two parts in the ratio 2 : 3.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the ratio of red paint to yellow paint in the new mixture?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio of orange juice to apple juice in its simplest form.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
The area of Delhi is 1,484 sq. km, and the area of Mumbai is 550 sq. km. The population of Delhi is approximately 30 million, and that of Mumbai is 20 million people. Which city is more crowded? Why do you say so?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Prashanti and Bhuvan started a food cart business near their school. Prashanti invested ₹ 75,000 and Bhuvan invested ₹ 25,000. At the end of the first month, they gained a profit of ₹ 4,000. They decided that they would share the profit in the same ratio as their investment. What is each person’s share of the profit?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
A crane of height 155 cm has its neck and the rest of its body in the ratio 4 : 6. For your height, if your neck and the rest of the body also had this ratio, how tall would your neck be?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Let us try an ancient problem from Lilavati. At that time, weights were measured in a unit named palas, and niskas was a unit of money. “If 212 \frac{1}{2}\;​palas of saffron costs 37 \;\frac{3}{7}\;​niskas, O expert businessman! Tell me quickly, what quantity of saffron can be bought for 9 niskas?”
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Harmain is a 1-year-old girl. Her elder brother is 5 years old. What will be Harmain’s age when the ratio of her age to her brother’s age is 1 : 2?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
It is good farming practice to apply 10 tonnes of cow manure for 1 acre of land. A farmer is planning to grow tomatoes in a plot of size 200 ft by 500 ft. How much manure should he buy? (Please refer to the section on Unit Conversions earlier in this chapter).
Proportional Reasoning-1 (New NCERT)
Medium
Q.
A tap takes 15 seconds to fill a mug of water. The volume of the mug is 500 mL. How much time does the same tap take to fill a bucket of water if the bucket has a 10-litre capacity?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
One acre of land costs ₹ 15,00,000. What is the cost of 2,400 square feet of the same land?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
A tractor can plough the same area of a field 4 times faster than a pair of oxen. A farmer wants to plough his 20-acre field. A pair of oxen takes 6 hours to plough an acre of land. How much time would it take if the farmer used a pair of oxen to plough the field? How much time would it take him if he decides to use a tractor instead?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
A mixture of 40 kg contains sand and cement in the ratio of 3 : 1. How much cement should be added to the mixture to make the ratio of sand to cement 5 : 2?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Puneeth’s father went from Lucknow to Kanpur in 2 hours by riding his motorcycle at a speed of 50 km/h. If he drives at 75 km/h, how long will it take him to reach Kanpur? Can we form this problem as a proportion 50 : 2 :: 75 : ____
Would it take Puneeth’s father more time or less time to reach Kanpur? Think about it.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Kesang wanted to make lemonade for a celebration. She made 6 glasses of lemonade in a vessel and added 10 spoons of sugar to the drink. Her father expected more people to join the celebration. So he asked her to make 18 more glasses of lemonade. To make the lemonade with the same sweetness, how many spoons of sugar should she add? How can we find the factor of change in the ratio?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Give 3 ratios that are proportional to 4 : 9.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Nitin and Hari were constructing a compound wall around their house. Nitin was building the longer side, 60 ft in length, and Hari was building the shorter side, 40 ft in length. Nitin used 3 bags of cement, but Hari used only 2 bags of cement. Nitin was worried that the wall Hari built would not be as strong as the wall he built because he used less cement. Is Nitin correct in his thinking?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
In my school, there are 5 teachers and 170 students. The ratio of teachers to students in my school is 5 : 170. Count the number of teachers and students in your school. What is the ratio of teachers to students in your school? Write it below. Is the teacher-to-student ratio in your school proportional to the one in my school?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Measure the width and height (to the nearest cm) of the blackboard in your classroom. What is the ratio of width to height of the blackboard?
Can you draw a rectangle in your notebook whose width and height are proportional to the ratio of the blackboard?
Compare the rectangle you have drawn to those drawn by your classmates. Do they all look the same?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
When Neelima was 3 years old, her mother was 10 times her age. What is the ratio of Neelima’s age to her mother’s age? What would be the ratio of their ages when Neelima is 12 years old? Would it remain the same?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Fill in the missing numbers for the following ratios that are proportional to 14 : 21.
(i) ____ : 42
(ii) 6 : ____
(iii) 2 : ____
What factor should we multiply 14 by to get 6? Can it be an integer? Or should it be a fraction?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Filter coffee is a beverage made by mixing coffee decoction with milk. Manjunath usually mixes 15 mL of coffee decoction with 35 mL of milk to make one cup of filter coffee in his coffee shop. In this case, we can say that the ratio of coffee decoction to milk is 15 : 35. If customers want ‘stronger’ filter coffee. Manjunath mixes 20 mL of the decoction with 30 mL of milk. The ratio here is 20 : 30. Why is this coffee stronger?
​(i) And when they want ‘lighter’ filter coffee, he mixes 10 mL of coffee and 40 mL of milk, making the ratio 10 : 40. Why is this coffee lighter?
(ii) The following table shows the different ratios in which Manjunath mixes coffee decoction with milk. Write in the last column if the coffee is stronger or lighter than the regular coffee.
Coffee Decoction (in mL)
Milk (in mL)
Regular/Strong/ Light
300
600

150
500

200
400

24
56

100
300

Proportional Reasoning-1 (New NCERT)
Medium
Q.
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
Proportional Reasoning-1 (New NCERT)
Medium
Q.
Fill in the missing numbers for these ratios that are proportional to 18 : 24.
(i) 3 : ________
(ii) 12 : ________
(iii) 20 : ________
(iv) 27 : ________
Proportional Reasoning-1 (New NCERT)
Medium
Q.
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.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
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.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
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?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
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.
Proportional Reasoning-1 (New NCERT)
Medium
Q.
For the mid-day meal in a school with 120 students, the cook usually makes 15 kg of rice. On a rainy day, only 80 students came to school. How many kilograms of rice should the cook make so that the food is not wasted?
The ratio of the number of students to the amount of rice needs to be proportional. So, 120 : 15 :: 80 : ?
What is the factor of change in the first term?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
(i) A car travels 90 km in 150 minutes. If it continues at the same speed, what distance will it cover in 4 hours?
If it continues at the same speed, the ratio of the time taken should be proportional to the ratio of the distance covered.
(ii) 150 : 90 :: 4 : x
Is this the right way to formulate the question?
(iii) How can you find the distance covered in 240 minutes?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
A small farmer in Himachal Pradesh sells each 200 g packet of tea for ₹ 200. A large estate in Meghalaya sells each 1 kg packet of tea for ₹ 800. Are the weight-to-price ratios in both places proportional? Which tea is more expensive? Why?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel in a week?
Proportional Reasoning-1 (New NCERT)
Medium
Q.
The ₹ 10 coin is an alloy of copper and nickel called ‘cupro-nickel’. Copper and nickel are mixed in a 3 : 1 ratio to get this alloy. The mass of the coin is 7.74 grams. If the cost of copper is ₹ 906 per kg and the cost of nickel is ₹ 1,341 per kg, what is the cost of these metals in a ₹ 10 coin?

NCERT Solutions For Class 8 Maths Chapter 7 Proportional Resoning

Q2. What is inverse proportion?

Answer: Two quantities are in inverse proportion when one increases, the other decreases.

Q3. If 5 pens cost ₹50, what is the cost of 8 pens?

Answer:
Cost of 1 pen = ₹50 ÷ 5 = ₹10
Cost of 8 pens = ₹10 × 8 = ₹80

Q4. If 4 workers complete a task in 12 days, how many days will 6 workers take?

Answer:
Workers and days are in inverse proportion.

4 × 12 = 6 × x
48 = 6x
x = 8 days

Q5. If 3 notebooks cost ₹90, what is the cost of 7 notebooks?

Answer:
Cost of 1 notebook = ₹90 ÷ 3 = ₹30
Cost of 7 notebooks = ₹30 × 7 = ₹210

Q6. A car travels 120 km in 3 hours. How far will it travel in 5 hours at same speed?

Answer:
Distance in 1 hour = 120 ÷ 3 = 40 km
Distance in 5 hours = 40 × 5 = 200 km

Q7. If 10 men build a wall in 6 days, how many days will 5 men take?

Answer:
10 × 6 = 5 × x
60 = 5x
x = 12 days

Q8. What is unitary method?

Answer: It is a method where we first find the value of one unit and then required units.

Q9. If 12 chocolates cost ₹144, what is cost of 5 chocolates?

Answer:
Cost of 1 chocolate = ₹144 ÷ 12 = ₹12
Cost of 5 chocolates = ₹12 × 5 = ₹60

Q10. Why is proportional reasoning important?

Answer: It helps solve real-life problems involving money, speed, work, and comparison of quantities.

FAQs

1. What is Chapter 7 of Class 8 Maths?

Chapter 7 of Class 8 Maths is Proportional Reasoning, based on direct and inverse proportion.

2. Why is this chapter important?

It builds concepts used in arithmetic, algebra, business maths, and daily calculations.

3. What is direct proportion?

When two quantities increase or decrease together in same ratio.

4. What is inverse proportion?

When one quantity increases while the other decreases.