CBSE Class 8 Mathematics Proportional Reasoning 1 Practice Paper Assignment Set 01 with Answers

Practice Paper 23 for Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 has 40 marks and 20 questions (Sections A–E), each answered step by step below. It tests similar notice boards, the ratio proportional to 81 : 108, a pump-filling time, chalk-packet costs, a brass–tin mixture, soil weight by volume, sharing ₹12500 in the ratio 19 : 6, bus speed, machine output, and case studies on a hospital kitchen's rice and the number of workers needed in a fabric cutting unit.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Reduce 252 : 378 to simplest form.
(b) Check whether 28 : 42 is proportional to it.
Answer:
(a) HCF of 252 and 378 is 126. So 252 : 378 = (252 ÷ 126) : (378 ÷ 126) = 2 : 3. Simplest form: 2 : 3.
(b) 28 : 42 = (28 ÷ 14) : (42 ÷ 14) = 2 : 3. Both ratios equal 2 : 3, so yes, 28 : 42 is proportional to 252 : 378.
Check by cross multiplication: 252 × 42 = 10584 and 378 × 28 = 10584, which are equal.
In simple words: Divide by the HCF to simplify; both ratios become 2 : 3, so they are proportional.

Teacher's Note:
1. Finding the HCF (126) in one step is faster than dividing again and again by small numbers.
2. Proportional means the two ratios are equal; cross products are equal too.

Question 12. (a) If 20 kg flour costs ₹840, find cost per kg.
(b) Find cost of 35 kg flour.
Answer:
(a) Cost per kg = ₹840 ÷ 20 = ₹42.
(b) Cost of 35 kg = 35 × ₹42 = ₹1470.
Check: 20 : 840 :: 35 : 1470, since 20 × 1470 = 840 × 35 = 29400.
In simple words: Find the price of 1 kg (₹42), then multiply by 35.

Teacher's Note:
1. This is the unitary method: first find the value of one unit, then of many units.
2. Cost and quantity are in direct proportion: double the kg, double the cost.

Question 13. (a) Find total parts in the ratio 19 : 6.
(b) Divide ₹12500 in this ratio.
Answer:
(a) Total parts = 19 + 6 = 25.
(b) Value of 1 part = ₹12500 ÷ 25 = ₹500.
First share = 19 × ₹500 = ₹9500.
Second share = 6 × ₹500 = ₹3000.
Check: ₹9500 + ₹3000 = ₹12500.
In simple words: Split ₹12500 into 25 equal parts and give 19 parts to the first and 6 parts to the second.

Teacher's Note:
1. To divide a quantity in a given ratio, first add the terms of the ratio.
2. Always check that the shares add up to the whole amount.

Question 14. (a) A bus travels 450 km in 9 hours. Find speed.
(b) Distance travelled in 14 hours.
Answer:
(a) Speed = distance ÷ time = 450 km ÷ 9 h = 50 km/h.
(b) At the same speed, distance in 14 hours = 50 × 14 = 700 km.
Check: 450 : 9 :: 700 : 14.
In simple words: The bus goes 50 km every hour, so in 14 hours it goes 700 km.

Teacher's Note:
1. At a constant speed, distance is directly proportional to time.
2. Write the unit km/h with speed and km with distance.

Section C: Short Answer Questions (3 Marks Each)

Question 15. (a) Simplify 132 : 198
(b) Simplify 20 : 30
(c) Check whether the two ratios are proportional
Answer:
(a) HCF of 132 and 198 is 66. 132 : 198 = (132 ÷ 66) : (198 ÷ 66) = 2 : 3. Answer: 2 : 3.
(b) HCF of 20 and 30 is 10. 20 : 30 = (20 ÷ 10) : (30 ÷ 10) = 2 : 3. Answer: 2 : 3.
(c) Both simplify to 2 : 3, so yes, they are proportional: 132 : 198 :: 20 : 30.
Cross-check: 132 × 30 = 3960 and 198 × 20 = 3960.
In simple words: Both ratios shrink to 2 : 3, so they are equal (proportional).

Teacher's Note:
1. Simplify each ratio fully before comparing.
2. Equal simplest forms, or equal cross products, both prove proportionality.

Question 16. (a) Total parts in the ratio 13 : 7
(b) Quantity of first part if total = 200 mL
(c) Quantity of second part
Answer:
(a) Total parts = 13 + 7 = 20.
(b) 1 part = 200 mL ÷ 20 = 10 mL. First part = 13 × 10 = 130 mL.
(c) Second part = 7 × 10 = 70 mL (or 200 − 130 = 70 mL).
Check: 130 : 70 = 13 : 7.
In simple words: Cut 200 mL into 20 equal parts of 10 mL; the first gets 13 parts and the second 7 parts.

Teacher's Note:
1. The fraction of the total for the first part is (first term) ÷ (sum of terms).
2. The second part can be found by subtracting the first part from the total.

Question 17. (a) A machine produces 1440 units in 18 hours. Rate per hour
(b) Units produced in 11 hours
(c) Time required to produce 2160 units
Answer:
(a) Rate = 1440 ÷ 18 = 80 units per hour.
(b) In 11 hours: 80 × 11 = 880 units.
(c) Time = 2160 ÷ 80 = 27 hours.
Check: 1440 : 18 :: 2160 : 27, since 1440 × 27 = 18 × 2160 = 38880.
In simple words: The machine makes 80 units each hour; multiply by hours to get units, divide units by 80 to get hours.

Teacher's Note:
1. Production and time are in direct proportion when the rate stays the same.
2. To find time, divide the work by the rate; to find work, multiply the rate by time.

Section D: Long Answer Question (5 Marks)

Question 18. A packaging unit packs 1750 boxes in 25 hours.
(a) Boxes packed per hour
(b) Boxes packed in 4 hours
(c) Boxes packed in 40 hours
(d) Time required to pack 2800 boxes
(e) Method used
Answer:
(a) Boxes packed per hour = 1750 ÷ 25 = 70 boxes.
(b) In 4 hours = 70 × 4 = 280 boxes.
(c) In 40 hours = 70 × 40 = 2800 boxes.
(d) Time = 2800 ÷ 70 = 40 hours.
(e) Unitary method (proportional reasoning): the quantity is directly proportional to the time, so we found the amount for 1 hour and then scaled it. For example, 25 : 1750 :: 40 : 2800.
In simple words: The unit packs 70 boxes an hour; 4 hours give 280 boxes, 40 hours give 2800 boxes, and 2800 boxes need 40 hours.

Teacher's Note:
1. Find the rate per hour once and reuse it for every part.
2. Parts (c) and (d) check each other: 40 hours ↔ 2800 boxes.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: Hospital Food Supply
A hospital kitchen prepares food daily. When 360 patients are served, 54 kg of rice is used. During an emergency, the number of patients increases to 480. To ensure uninterrupted food supply and equal distribution, the kitchen manager calculates the total rice required using proportional reasoning.
Answer the following questions:
(a) Rice used per patient
(b) Write the proportion
(c) Rice required for 480 patients
(d) Extra rice required
Answer:
(a) Rice per patient = 54 kg ÷ 360 = \( \frac{3}{20} \) kg = 0.15 kg (150 g).
(b) Patients : rice stays the same, so 360 : 54 :: 480 : x, where x kg is needed for 480 patients.
(c) x = \( \frac{54 × 480}{360} \) = 72 kg (or 480 × 0.15 = 72 kg).
(d) Extra rice = 72 − 54 = 18 kg.
Check: 120 more patients × 0.15 kg = 18 kg.
In simple words: Each patient gets 0.15 kg, so 480 patients need 72 kg, that is 18 kg more.

Teacher's Note:
1. Equal distribution means rice is directly proportional to the number of patients.
2. Writing 360 : 54 :: 480 : x keeps patients first and rice second on both sides.

Question 20. Case Study 2: Fabric Cutting Unit
A tailoring unit cuts 420 metres of fabric using 14 workers in one day. For a larger order requiring 750 metres of fabric under the same working conditions, the supervisor estimates the number of workers required using proportional reasoning to complete the work on time.
Answer the following questions:
(a) Fabric cut per worker
(b) Write the proportion
(c) Workers required for 750 metres
(d) Additional workers required
Answer:
(a) Fabric cut per worker in a day = 420 m ÷ 14 = 30 m.
(b) Fabric : workers stays the same, so 420 : 14 :: 750 : x, where x is the number of workers for 750 m.
(c) x = \( \frac{14 × 750}{420} \) = 25 workers (or 750 ÷ 30 = 25).
(d) Additional workers = 25 − 14 = 11 workers.
In simple words: One worker cuts 30 m a day, so 750 m needs 25 workers, which is 11 more than the 14 already working.

Teacher's Note:
1. In one day, the fabric cut is directly proportional to the number of workers.
2. Answers about people must be whole numbers; here 750 ÷ 30 = 25 exactly.