Average, Ratio & Proportion, Percentage Quiz - ICSE Class 6 Mathematics

Free practice quiz: Average, Ratio & Proportion, Percentage (ICSE Class 6 Mathematics). 45 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 6 Mathematics practice quiz has 45 multiple-choice questions on Average, Ratio & Proportion, Percentage, and 45 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. The ratio of two numbers is 3:5. If the sum of the numbers is 80, find the numbers.

   1. 25 and 55
   2. 30 and 50
   3. 24 and 56
   4. 35 and 45
   Show answer

   Answer: B. 30 and 50

   Let the two numbers be 3x and 5x, as their ratio is 3:5. The sum of the numbers is given as 80. So, 3x + 5x = 80. This simplifies to 8x = 80. Dividing by 8, we get x = 10. The two numbers are therefore 3x = 3 * 10 = 30 and 5x = 5 * 10 = 50. We can check this: 30 + 50 = 80 and the ratio 30:50 simplifies to 3:5. Thus, the numbers are 30 and 50.

2. If the ratio of the cost price to the selling price of an article is 5:6, then the percentage of profit is:

   1. 10%
   2. 15%
   3. 20%
   4. 25%
   Show answer

   Answer: C. 20%

   Let the cost price (CP) be 5x and the selling price (SP) be 6x, as their ratio is 5:6. The profit is the difference between the selling price and the cost price: Profit = SP - CP = 6x - 5x = x. To calculate the percentage of profit, we use the formula: Percentage Profit = (Profit / CP) * 100. Percentage Profit = (x / 5x) * 100. Percentage Profit = (1/5) * 100 = 20%. Therefore, the percentage of profit is 20%.

3. The ratio of apples to oranges in a basket is 5:3. If there are 32 fruits in total, how many apples are there?

   1. 15
   2. 18
   3. 20
   4. 24
   Show answer

   Answer: C. 20

   Let the number of apples be 5x and the number of oranges be 3x, based on the ratio 5:3. The total number of fruits is the sum of apples and oranges: 5x + 3x = 32. This simplifies to 8x = 32. Dividing by 8, we get x = 4. The number of apples is 5x, so there are 5 * 4 = 20 apples. The number of oranges is 3x, so there are 3 * 4 = 12 oranges. Check: 20 apples + 12 oranges = 32 fruits. The ratio of apples to oranges is 20:12, which simplifies to 5:3. Thus, there are 20 apples.

4. If 60% of a number is 90, what is 40% of that number?

   1. 50
   2. 55
   3. 60
   4. 65
   Show answer

   Answer: C. 60

   Let the number be 'N'. We are given that 60% of N is 90. So, (60/100) * N = 90. This means 0.6 * N = 90. To find N, divide 90 by 0.6: N = 90 / 0.6 = 900 / 6 = 150. Now we need to find 40% of 150. 40% of 150 = (40/100) * 150 = 0.4 * 150 = 60. Therefore, 40% of the number is 60.

5. If a number is decreased by 10% and then increased by 10%, what is the net percentage change?

   1. 1% decrease
   2. 1% increase
   3. 0% change
   4. 10% decrease
   Show answer

   Answer: A. 1% decrease

   Let the original number be 100. When it is decreased by 10%, the new number becomes 100 - (10% of 100) = 100 - 10 = 90. When this new number (90) is increased by 10%, the increase amount is 10% of 90. 10% of 90 = (10/100) * 90 = 0.1 * 90 = 9. The new number after the increase is 90 + 9 = 99. The original number was 100, and the final number is 99. The net change is 99 - 100 = -1. This means there is a decrease of 1. As a percentage of the original number: (1 / 100) * 100 = 1%. So, there is a net 1% decrease. Using the shortcut formula: Net % Change = (x + y + xy/100)%. Here, x = -10% (decrease) and y = +10% (increase). Net % Change = (-10 + 10 + (-10 * 10) / 100)% = (0 + (-100) / 100)% = (0 - 1)% = -1%. A negative sign indicates a decrease.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If 60% of a number is 45, then what is 80% of that number?
2. The average of the first 7 natural numbers is:
3. Two numbers are in the ratio 5:8. If the difference between the numbers is 24, find the numbers.
4. A shopkeeper sells a shirt for $450, making a profit of 25%. What was the cost price of the shirt?
5. The average age of 3 boys is 14 years. If the age of the youngest boy is 10 years and the age of the oldest boy is 18 years, what is the age of the middle boy?
6. The ratio of boys to girls in a class is 7:5. If there are 35 boys in the class, how many girls are there?
7. What is 75% of 200?
8. The average of 6 numbers is 15. If one number is excluded, the average of the remaining 5 numbers is 14. What is the excluded number?
9. A person spends 30% of their income on rent and 15% on food. What percentage of their income is left?
10. The average of 10 numbers is 20. If each number is increased by 5, what will be the new average?
11. In a class, the ratio of the number of girls to the number of boys is 4:3. If there are 28 students in total, how many boys are there?
12. If 40% of a number is 120, what is 60% of that same number?
13. The average of 5 numbers is 32. If one number is removed, the average of the remaining 4 numbers is 30. What is the removed number?
14. Two numbers are in the ratio 2:3. If the sum of their squares is 117, find the numbers.
15. What is 12.5% of 800?
16. The average of 8 numbers is 45. If the average of the first 4 numbers is 40, what is the average of the remaining 4 numbers?
17. If 70% of a number is 140, what is 90% of that number?
18. The average score of 5 students in a test was 78. If one student's score is removed, the average of the remaining 4 students is 75. What was the score of the removed student?
19. The ratio of two numbers is 7:11. If the difference between the numbers is 32, find the numbers.
20. A shopkeeper buys an article for $200 and sells it for $250. What is the percentage profit?
21. If the ratio of the length to the width of a rectangle is 5:3, and its perimeter is 48 cm, what is its area?
22. A student scored 75% marks in an exam. If the maximum marks were 600, how many marks did the student score?
23. The average of 5 numbers is 28. If one number is removed, the average becomes 26. What is the removed number?
24. The ratio of Ram's salary to Shyam's salary is 4:5. If Shyam's salary is $5000, what is Ram's salary?
25. A mixture contains milk and water in the ratio 5:2. If the total volume of the mixture is 700 ml, what is the volume of milk in the mixture?
26. By what percentage is 500 greater than 400?
27. The average of the first 10 positive integers is:
28. If 30% of a number is 75, what is 80% of that number?
29. The ratio of ages of father and son is 7:2. If the sum of their ages is 54 years, find the age of the father.
30. A number is increased by 20% and then decreased by 20%. What is the net percentage change?
31. The ratio of boys to girls in a school is 5:4. If the total number of students is 540, find the number of girls.
32. The average of the first 5 odd numbers is:
33. The ratio of the cost price to the selling price of a fan is 4:5. What is the percentage of profit?
34. A shopkeeper bought a table for $600 and sold it for $720. What was his profit percentage?
35. The ratio of two numbers is 9:5. If the sum of the numbers is 140, find the numbers.
36. The average of 5 numbers is 42. If one number is removed, the average of the remaining 4 numbers is 40. What is the removed number?
37. What is 15% of 300?
38. The ratio of two numbers is 3:7. If the sum of the numbers is 100, find the numbers.
39. The average of 12 numbers is 50. If each number is decreased by 3, what will be the new average?
40. A dealer sells a watch for $300, making a profit of 20%. What was the cost price of the watch?

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