Important Questions for Class 8 Maths Chapter 7 Comparing Quantities

Important Question Class 8 Maths Chapter 8 Comparing Quantities

Here are important questions from Chapter 8  Comparing Quantities for Class 8 Maths along with their solutions:

Q.1. If the ratio of the number of boys to girls in a class is 5:3, find the number of boys and girls if there are 30 students in total.

Solution:

Let the number of boys be 5x and girls be 3x. Total = 5x + 3x = 30. $x=3$ . Boys = 15, Girls = 9.

Q.2. A shopkeeper marks the price of an article 25% above the cost price and allows a discount of 10% on the marked price. Find the selling price of the article.

Solution:

Marked Price = 125, Discount = 12.5. Selling Price = 112.5.

Q.3. If the price of an article increases by 20% and then decreases by 10%, what is the net percentage change in its price?

Solution:

Increase by 20% gives new price = 120. Decrease by 10% gives final price = 108. Net change = 8%.

Q.4. A person invested Rs. 8000 in two schemes A and B. He invested twice as much in A as in B. How much did he invest in each scheme?

Solution:

Let x be invested in B. A = 2x. Total = 8000. $x=2666.67$ . A = 5333.33, B = 2666.67.

Q.5. If 72% of 25 students like maths, find out the number of students who do not like mathematics?

Solution:

Given, 72% of 25 students like maths. Hence, 72% of 25 = (72/100) × 25 = 18 students Now, from 25 students, 18 students like maths Thus, the number of students who do not like maths = 25 – 18 = 7 students

Q.6. A person goes shopping and spends 75% of his money. If he is now left with Rs. 600, find out how much he had in the beginning.

Solution:

Let “x” be the initial amount that he had in the beginning. As per the given question, the person spent 75% of Rs.x and is left with Rs. 600. So, the amount he spent = x – 600 => 75% of x = x – 600 => (75/100) × x = x – 600 => 75x = 100x – 60,000 =>25x = 60,000 Or, x = 2400. Thus, the person had Rs. 2400 initially.

Q.7. A shopkeeper bought two phones for Rs. 8,000 each. After selling the phones, there was a loss of 4% on the 1st phone while a profit of 8% on the 2nd phone. Calculate the overall gain or loss per cent on the whole transaction.

Solution:

As the shopkeeper bought both phones at Rs. 8000 each. Total cost price = Rs. 16,000 Assume that the cost price of the 1st phone is Rs. 100 Consider the deal of phone 1, As it is given, there is 4% loss, the selling price will be = Rs. 96 For CP = 100, SP = 96 So, for CP = 1, SP = 96/100 Now, given, CP = 8000 Hence, SP = 96/100 × 8000 = 7680 Thus, the selling price of 1st phone = Rs. 7680 Consider the deal of phone 2, there is an 8% profit. Hence, the selling price will be = Rs. 108 For CP = 100, SP = 108 So, for CP = 1, SP = 108/100 Now, given CP = 8000 hence, SP = 108/100 × 8000 = 8640 Thus, the selling price of 2nd phone = Rs. 8640 Here, the total selling price will be = Rs. 7680 + Rs. 8640 = 16320 Now, it can be seen that, Total selling price > total cost price i.e. Rs. 16320 > Rs. 16000 So, there is a profit of Rs. (16320 – 16000) = Rs. 320 Now, the overall profit percentage will be- Profit% = (Profit/Total Cost Price) × 100 = (320/16000) × 100 = 2 Therefore, there is a total of 2% profit for the whole transaction.

Q.8. 72% of 25 students are good in mathematics. How many are not good in mathematics?

Solution:

Total number of students = 25 Number of good students in mathematics = 72% of 25 $=\frac{72}{100}\times 25=18$ $\therefore$ Number of students not good in mathematics = 25 - 18 = 7

Q.9. If apples are bought at 11 for RS 10 & sold at 10 for RS 11.

Solution:

Benefits of Solving Important Questions for Class 8 Maths Chapter 7

• Understanding Key Concepts: These questions cover essential topics like ratios, percentages, and proportions, helping students to grasp the underlying concepts thoroughly.
• Exam Preparation: Practicing these questions prepares students for their exams by familiarizing them with the types of questions that are likely to appear. This boosts confidence and improves their problem-solving skills.
• Application of Concepts: The questions often require applying mathematical concepts to real-world problems, which enhances critical thinking and the ability to solve practical problems.
• Improved Problem-Solving Skills: Working through different types of questions helps students improve their problem-solving speed and accuracy. They learn how to approach and solve complex questions more effectively.
• Building Mathematical Foundation: Regular practice of these important questions strengthens the foundational knowledge necessary for higher-level mathematics. It helps in retaining concepts and formulas better.
• Identifying Strengths and Weaknesses: By solving these questions, students can identify areas where they are strong and where they need to improve, allowing them to focus their study efforts more efficiently.

Important Questions for Class 8 Maths Chapter 1	Important Questions for Class 8 Maths Chapter 2
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Important Questions for Class 8 Maths Chapter 5	Important Questions for Class 8 Maths Chapter 6
Important Questions for Class 8 Maths Chapter 7	Important Questions for Class 8 Maths Chapter 8
Important Questions for Class 8 Maths Chapter 9	Important Questions for Class 8 Maths Chapter 10
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