Ganita Prakash | Grade 8 Mock Test: Chapter 7 - Proportional Reasoning-1

Mock Test: Chapter 7 - Proportional Reasoning-1

Grade 8 Mathematics

Name: _________________ Date: _________________ Time: 60 minutes

Instructions:

• Answer all questions
• Show your working clearly
• Write answers in the space provided
• Use cross-multiplication where appropriate

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Section A: Multiple Choice Questions (1 mark each)

1. Which of the following ratios is equivalent to 15:25?
a) 3:5
b) 5:3
c) 6:10
d) 12:18

2. If 4:7 :: 12:x, then the value of x is:
a) 21
b) 18
c) 24
d) 28

3. The ratio 48:72 in its simplest form is:
a) 6:9
b) 2:3
c) 4:6
d) 8:12

4. If a quantity is divided in the ratio 3:5, and the total quantity is 240, the smaller part is:
a) 90
b) 120
c) 150
d) 100

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Section B: Short Answer Questions (2 marks each)

5. Check whether the ratios 18:24 and 27:36 are proportional. Show your work by reducing to simplest form.

6. If 6 pens cost ₹84, find the cost of 9 pens using proportional reasoning.

7. A recipe calls for 4 cups of flour and 3 cups of sugar. If Maria wants to use 12 cups of flour, how much sugar should she use?

8. Convert the following units using proportional reasoning:

• 3 hours 45 minutes = _______ minutes

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Section B: Long Answer Questions (4 marks each)

9. Kesang's Juice Problem (Similar to Example 2)
Kesang makes orange juice by mixing 5 glasses of water with 8 spoons of orange concentrate. If she wants to make 20 glasses of orange juice, how many spoons of concentrate will she need? Show two different methods to solve this problem.

10. Sharing Profit Problem
Three friends Amit, Bina, and Chetan invested ₹15,000, ₹25,000, and ₹35,000 respectively in a small business. At the end of the year, they made a profit of ₹22,500. How should this profit be shared among them in proportion to their investments?

11. Construction Problem (Similar to Example 3)
Builder A uses 8 bags of cement for every 12 meters of wall length. Builder B uses 10 bags of cement for every 15 meters of wall length. Which builder uses cement more efficiently (uses less cement per meter)? Show your calculations.

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Section C: Application Problems (5 marks each)

12. Recipe Adjustment Problem
A cake recipe for 8 people requires:

• 400g flour
• 200g sugar
• 6 eggs
• 150ml milk

Priya wants to make the same cake for 12 people. Calculate the amount of each ingredient she will need. Show your working using cross-multiplication.

13. Map Scale Problem
On a map, 2 cm represents 5 km of actual distance.
a) If two cities are 7.5 cm apart on the map, what is the actual distance between them?
b) If the actual distance between two towns is 37.5 km, how far apart will they appear on the map?
Show all calculations using proportional reasoning.

14. Mixture Problem (Similar to Example 12)
A concrete mixture contains sand and cement in the ratio 5:2.
a) If there are 35 kg of sand in the mixture, how much cement is there?
b) How much more cement should be added to change the ratio to 5:3?
Show complete working.

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Section D: Critical Thinking (6 marks)

15. Real-life Application
You are planning a school picnic. Based on past experience, you know that:

• 30 students require 12 liters of juice
• 30 students need 45 sandwiches
• 30 students generate 18 kg of waste

If 125 students are going on the picnic:
a) How much juice will you need?
b) How many sandwiches should you prepare?
c) How much waste should you expect?
d) Explain why proportional reasoning is useful in this planning scenario.

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Bonus Question (2 marks)

16. Historical Connection
The ancient Indian mathematician Āryabhața developed the "Rule of Three" over 1500 years ago. If using his formula where Unknown = (phala × ichchhā)/pramāņa, solve this problem:
If 7 books cost ₹210, what will 11 books cost?
Identify what represents phala, ichchhā, and pramāņa in this problem.

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Answer Key Summary:

1. a) 3:5
2. a) 21
3. b) 2:3
4. a) 90
5. Both simplify to 3:4, so proportional
6. ₹126
7. 9 cups sugar
8. 225 minutes
9. 32 spoons (factor method: ×4, cross-multiplication: 5×32=8×20)
10. Amit: ₹4,500, Bina: ₹7,500, Chetan: ₹10,500
11. Both use 2/3 bags per meter - equally efficient
12. 600g flour, 300g sugar, 9 eggs, 225ml milk
13. a) 18.75 km, b) 15 cm
14. a) 14 kg cement, b) 7 kg more cement
15. a) 50L juice, b) 187.5≈188 sandwiches, c) 75 kg waste, d) Ensures adequate resources
16. ₹330; phala=₹210, ichchhā=11, pramāņa=7