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Fractions in Disguise - Exercise 1.3 Class 8 Maths - Chapter 1 NCERT Solutions

Class 8 Maths NCERT Ganita Prakash Term 2 Chapter 1 Fractions in Disguise Exercise 1.3 detailed solutions are prepared by the expert mentors at ALLEN, following the updated NCERT syllabus. The solutions make the learning process simple and effective, helping students understand the questions and methods covered in the exercise for their final exams.Exercise 1.3 emphasises mainly on using percentages to understand and solve quantity-based situations, such as finding the original quantity when a percentage and its corresponding quantity are given, calculating the selling price when a profit margin is given, working with percentage increase and decrease, calculating discounts, and applying GST to prices.

1.0Download Class 8 Maths Chapter 1 Ex 1.3 NCERT Solutions PDF

Download the detailed solutions for Ganita Prakash Term 2 Chapter 1, Fractions in Disguise Exercise 1.3, provided here for better understanding and effective learning.

Chapter 1 : Fractions in Disguise Exercise 1.3

2.0Detailed NCERT Solutions on Fractions in Disguise Exercise 1.3 Class 8 Maths (Ganita Prakashan Term 2)

1. If a shopkeeper buys a geometry box of ₹75 and sells it for ₹110, what is his profit margin with respect to the cost?

Sol. Profit $= ₹110 - ₹75 = ₹35$ Profit % = $\frac{35}{75} \times 100$ $= 0.4667 \times 100 = 46.67%$

2. I am a carpenter, and I make chairs. The cost of materials for a chair is ₹475, and I want to have a profit margin of $50%$ . At what price should I sell a chair?

Sol. Cost of material $=$ ₹475 Profit $= 50%$ of 475 $= \frac{50}{100} \times 475 = ₹237.50$ Sale price $= ₹475 + ₹237.50 = ₹712.50$

3. The total sales of a company (also called revenue) were ₹2.5 crore last year. They had a healthy profit margin of $25%$ . What was the total expenditure (costs) of the company last year?

Sol. Let the total expenditure (cost) be x Then profit $= ₹ \frac{25 x}{100}$ or $₹0.25 x$ $∴$ Revenue $= x + 0.25 x = 2.5$ crores $\Rightarrow 1.25 x = 2.5$ $\Rightarrow x = \frac{2.5}{1.25} = \frac{250}{125} = 2$ ∴ The total expenditure of the company is ₹2 crore

4. A clothing shop offers a $25%$ discount on all shirts. If the original price of a shirt is ₹300, how much will Anwar have to pay to buy this shirt?

Sol. Marked price $= ₹300$ Discount $= ₹ \frac{25}{100} \times 300 = ₹75$ Sale price = ₹300 - ₹75 = ₹225

5. The petrol price in 2015 was ₹60 and ₹100 in 2025. What is the percentage increase in the price of petrol? (i) $50%$ (ii) $40%$ (iii) $60%$ (iv) $66.66%$ (v) $140%$ (vi) $160.66%$

Sol. Increase in price $= ₹100 - ₹60 = ₹40$ Increase $% = \frac{40}{60} \times 100% = 66 \frac{2}{3} %$ or 66.66%

6. Samson bought a car for ₹4,40,000 after getting a 15% discount from the car dealer. What was the original price of the car?

Sol. Let the marked price of the car be ₹x Discount $= \frac{15}{100} x = 0.15 x$ Sale price $= x - 0.15 x = 0.85 x$ Now $0.85 x = 4, 40, 000$ $x = \frac{4 , 40 , 000}{0.85} = 517647$ Marked price of the car is ₹5,17,647.

7. 1600 people voted in an election, and the winner got 500 votes. What percent of the total votes did the winner get? Can you guess the minimum number of candidates who stood for the election?

Sol. Vote $%$ (winner) $= \times 100% = 31.25%$ and $100 \div 31.25 = 3.2$ ∴ In all, there were at least 4 candidates. This means at least 3 more candidates.

8. The price of 1 kg of rice was ₹38 in 2024. It is ₹42 in 2025. What is the rate of inflation? (Inflation is the percentage increase in prices.) Sol. Increase in price $= ₹42 - ₹38 = ₹4$ Rate of inflation $= \frac{4}{38} \times 100% = 10.52%$

9. A number increased by $20%$ becomes 90. What is the number? Sol. 120% of a number is 90 $∴ 1%$ of the number is $\frac{90}{120}$ $100%$ of the number $= \frac{90}{120} \times 100 = 75$ Therefore, the number was 75.

10. A milkman sold two buffaloes for ₹80,000 each. On one of them, he made a profit of $5%$ and on the other a loss of $10%$ . Find his overall profit or loss. Sol. SP of $1^{st}$ buffalo $= ₹80, 000$ Profit% = 5% $∴ CP = ₹ \frac{100}{100 + 5} \times 80, 000 = ₹76, 190$ SP of $2^{nd}$ buffalo $= ₹80, 000$ Loss % $= 10$ % $∴ CP = ₹ \frac{100}{100 - 10} \times 80, 000 = ₹88, 889$ Total CP = ₹76,190 + ₹88,889 = ₹1,65,079 Total SP = ₹80,000 + ₹80,000 = ₹1,60,000 Loss $=$ ₹1,65,079 - ₹1,60,000 = ₹5,079 $Loss % = \frac{5079}{165079} \times 100% = 3%$

11. The population of elephants in a national park increased by 5% in the last decade. If the population of the elephants over the last decade is p , the population now is (i) $p \times 0.5$ (ii) $p \times 0.05$ (iii) $p \times 1.5$ (iv) $p \times 1.05$ (v) $p + 1.50$

Sol. (iv) $p \times 1.05$ Population 10 years ago = p Increase in population $= \frac{5}{100} P = 0.05 p$ $∴$ Current population $= p + 0.05 p = 1.05 p$

12. Which of the following statements(s) means the same as - "The demand for cameras has fallen by $85%$ in the last decade"? (i) The demand now is $85%$ of the demand a decade ago. (ii) The demand a decade ago was $85%$ of the demand now. (iii) The demand now is $15%$ of the demand a decade ago. (iv) The demand a decade ago was $15%$ of the demand now. (v) The demand a decade ago was 185% of the demand now. (vi) The demand now is $185%$ of the demand a decade ago. Sol. Statement: The demand for cameras has fallen by 85% in last decade. Only (iii) means the same.

3.0Key Concepts of Chapter 1- Fractions in Disguise Exercise 1.3

Finding percentage increase and percentage decrease in quantities.
Calculating profit and profit margin using percentages.
Finding the selling price when the profit percentage is given.
Calculating discounts and the price after applying a discount.
Applying GST and other percentage-based taxes to a given price.
Comparing quantities or values using percentage relationships.
Solving real-life problems involving profit, discounts, taxes, and percentage changes.

4.0Benefits of NCERT Solutions Class 8 Maths Chapter 1 Exercise 1.3

Explains how percentage increase and decrease are calculated from the original value.
Shows the difference between profit percentage and profit margin in the given problems.
Breaks down calculations involving cost price, selling price, and profit percentage.
Explains how a discount percentage changes the marked price and final selling price.
Shows how GST percentage is applied to calculate the final price.
Helps solve multi-step questions where profit, discount, or tax percentages are applied successively.
Clarifies percentage-based comparisons and changes in real-life pricing situations.

NCERT Class 8 Maths Ch. 1 Fractions in Disguise Other Exercises:-

Exercise 1.1

Exercise 1.2