Q1
1 Mark
What is 25% of 200?
A50
B25
C75
D100
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Correct answer: Option 1 — 50
Chapter 2 · Class 7 Mathematics
Comparing Quantities — Important Questions
SUMMARY: The chapter "Comparing Quantities" focuses on understanding and solving problems related to ratios, percentages, and their applications in real-life situations.
KEY TOPICS: ratios, percentages, percentage increase and decrease, profit and loss, simple interest, converting fractions to percentages, converting percentages to fractions, applications of percentages in real-life scenarios
Multiple Choice Questions (MCQs)
5 questions
Q2
1 Mark
If a shirt originally costs ₹800 and is on sale for ₹600, what is the percentage decrease in price?
A25%
B20%
C30%
D15%
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Correct answer: Option 1 — 25%
Q3
1 Mark
A car was bought for ₹1,00,000 and sold for ₹1,20,000. What is the profit percentage?
A15%
B20%
C25%
D30%
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Correct answer: Option 2 — 20%
Q4
1 Mark
Convert 0.75 into a percentage.
A75%
B70%
C80%
D65%
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Correct answer: Option 1 — 75%
Q5
1 Mark
If you invest ₹10,000 at a simple interest rate of 5% per annum, how much interest will you earn in 3 years?
A₹1,500
B₹1,000
C₹1,200
D₹1,500
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Correct answer: Option 2 — ₹1,000
Short Answer Questions
5 questions
Q6
3 Marks
A shopkeeper bought a shirt for ₹500 and sold it for ₹600. What is the profit percentage?
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The profit is ₹600 - ₹500 = ₹100. The profit percentage is (Profit/Cost Price) × 100 = (100/500) × 100 = 20%.
Q7
3 Marks
Convert 75% into a fraction. Simplify your answer.
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75% can be written as 75/100. Simplifying this gives 3/4.
Q8
3 Marks
If a population of a town increases from 20,000 to 25,000, what is the percentage increase in population?
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The increase in population is 25,000 - 20,000 = 5,000. The percentage increase is (5,000/20,000) × 100 = 25%.
Q9
3 Marks
A student scored 45 out of 60 in a test. What is the percentage score?
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The percentage score is (45/60) × 100 = 75%.
Q10
3 Marks
If a loan of ₹10,000 is taken at a simple interest rate of 5% per annum, how much interest will be paid after 3 years?
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The simple interest is calculated as SI = Principal × Rate × Time = 10,000 × 5/100 × 3 = ₹1,500.
Long Answer Questions
5 questions
Q11
6 Marks
A shopkeeper bought a shirt for Rs. 500 and sold it for Rs. 650. Calculate the profit percentage. Explain the steps you used to find the percentage.
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To find the profit percentage, first calculate the profit by subtracting the cost price from the selling price. Profit = Selling Price - Cost Price = 650 - 500 = Rs. 150. Next, to find the profit percentage, use the formula: (Profit / Cost Price) x 100. Thus, Profit Percentage = (150 / 500) x 100 = 30%. Therefore, the profit percentage is 30%.
Q12
6 Marks
A student scored 80 out of 100 in Mathematics and 70 out of 100 in Science. Calculate the overall percentage of marks obtained by the student. Discuss how you arrived at the final percentage.
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To calculate the overall percentage, first find the total marks obtained and the total possible marks. The total marks obtained = 80 + 70 = 150, and the total possible marks = 100 + 100 = 200. Now, use the percentage formula: (Total Marks Obtained / Total Possible Marks) x 100. Therefore, Overall Percentage = (150 / 200) x 100 = 75%. The student has an overall percentage of 75%.
Q13
6 Marks
A car's value depreciates by 15% each year. If the current value of the car is Rs. 2,00,000, what will be its value after 3 years? Show your calculations and explain the concept of percentage decrease.
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To calculate the value of the car after 3 years with a depreciation of 15% per year, first find the value after the first year: Value after 1 year = Current Value - (15% of Current Value) = 200000 - (0.15 x 200000) = 200000 - 30000 = Rs. 170000. Repeat this for the next two years: After 2 years = 170000 - (0.15 x 170000) = 170000 - 25500 = Rs. 144500. After 3 years = 144500 - (0.15 x 144500) = 144500 - 21675 = Rs. 122825. Thus, the value of the car after 3 years will be Rs. 122825.
Q14
6 Marks
A bank offers a simple interest rate of 5% per annum. If you invest Rs. 10,000 for 4 years, calculate the total interest earned and the total amount at the end of the investment period. Explain your calculations.
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To calculate the simple interest earned, use the formula: Simple Interest = (Principal x Rate x Time) / 100. Here, Principal = Rs. 10,000, Rate = 5%, and Time = 4 years. Therefore, Simple Interest = (10000 x 5 x 4) / 100 = Rs. 2000. To find the total amount at the end of the investment period, add the interest to the principal: Total Amount = Principal + Simple Interest = 10000 + 2000 = Rs. 12000. Thus, the total interest earned is Rs. 2000 and the total amount is Rs. 12000.
Q15
6 Marks
A recipe requires 2 cups of sugar for every 5 cups of flour. If you want to make a larger batch using 15 cups of flour, how much sugar will you need? Explain the ratio and how you calculated the amount of sugar needed.
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The ratio of sugar to flour in the recipe is 2:5. To find out how much sugar is needed for 15 cups of flour, set up a proportion based on the ratio. If 5 cups of flour require 2 cups of sugar, then for 15 cups of flour, the amount of sugar needed can be calculated as follows: (2/5) = (x/15). Cross-multiply to find x: 2 * 15 = 5 * x, which gives 30 = 5x. Solving for x gives x = 30/5 = 6. Therefore, you will need 6 cups of sugar for 15 cups of flour.
Assertion–Reason Questions
5 questions
Q16
1 Mark
Assertion (A): A ratio of 3:4 can be expressed as a percentage of 75%.
Reason (R): To convert a ratio to a percentage, you multiply by 100 and divide by the sum of the parts.
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Correct answer: Option 3 —
A is true, but R is false.
Q17
1 Mark
Assertion (A): If a product's price increases from ₹200 to ₹250, the percentage increase is 25%.
Reason (R): Percentage increase is calculated by the formula ((new value - old value) / old value) * 100.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q18
1 Mark
Assertion (A): A loss of 20% means the selling price is less than the cost price.
Reason (R): A loss percentage indicates that the selling price is lower than the cost price.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q19
1 Mark
Assertion (A): Simple interest can be calculated using the formula SI = (P * R * T) / 100.
Reason (R): The formula for simple interest is derived from the principal amount, rate of interest, and time period.
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Correct answer: Option 2 —
Both A and R are true, but R is not the correct explanation of A.
Q20
1 Mark
Assertion (A): Converting a fraction to a percentage involves multiplying the fraction by 100.
Reason (R): To convert a fraction to a percentage, you multiply by 100 and add the percentage sign.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Statement-Based Questions
5 questions
Q21
1 Mark
Statement 1: A ratio of 3:4 can be expressed as a percentage of 75%.
Statement 2: A percentage increase of 20% on a quantity of 50 results in a new quantity of 60.
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Correct answer: Option 3 —
Only Statement 2 is true.
Q22
1 Mark
Statement 1: If a shirt originally costs ₹500 and is sold for ₹450, the percentage loss is 10%.
Statement 2: The simple interest on a principal of ₹1000 at a rate of 5% for 2 years is ₹100.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q23
1 Mark
Statement 1: To convert a fraction 1/4 into a percentage, you multiply by 100.
Statement 2: A percentage decrease of 30% on a quantity of 200 results in a new quantity of 140.
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Correct answer: Option 1 —
Both statements are true.
Q24
1 Mark
Statement 1: If the cost price of an item is ₹800 and the selling price is ₹960, the profit percentage is 20%.
Statement 2: A decrease of 25% on a quantity of 80 results in a new quantity of 60.
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Correct answer: Option 4 —
Both statements are false.
Q25
1 Mark
Statement 1: A percentage of 150% means the whole quantity plus an additional half of it.
Statement 2: If a bank offers simple interest of 10% per annum, the total amount after 3 years on ₹2000 will be ₹2600.
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Correct answer: Option 2 —
Only Statement 1 is true.
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