CBSE Class 8 Mathematics Proportional Reasoning 1 Practice Paper Assignment Set 02 with Answers

Class 8 Maths Ganita Prakash Chapter 7 Proportional Reasoning-1 Practice Paper 25 is a 40-mark paper of 20 questions in five sections, given here with a worked answer for each one. It asks about similar banners, a ratio proportional to 48 : 64, grains for 216 people, a motor pump, biscuit packets, a copper–zinc alloy, dividing ₹8000 in the ratio 11 : 9, a cyclist's speed, a printing press's output, and case studies on relief camp rice and the bricks needed to extend a wall.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Reduce 126 : 189 to simplest form.
(b) Check whether 14 : 21 is proportional to it.
Answer:
(a) HCF of 126 and 189 is 63. So 126 : 189 = (126 ÷ 63) : (189 ÷ 63) = 2 : 3. Simplest form: 2 : 3.
(b) 14 : 21 = (14 ÷ 7) : (21 ÷ 7) = 2 : 3. Both ratios equal 2 : 3, so yes, 14 : 21 is proportional to 126 : 189.
Check by cross multiplication: 126 × 21 = 2646 and 189 × 14 = 2646, 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 (63) 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 15 kg potatoes cost ₹450, find cost per kg.
(b) Find cost of 22 kg potatoes.
Answer:
(a) Cost per kg = ₹450 ÷ 15 = ₹30.
(b) Cost of 22 kg = 22 × ₹30 = ₹660.
Check: 15 : 450 :: 22 : 660, since 15 × 660 = 450 × 22 = 9900.
In simple words: Find the price of 1 kg (₹30), then multiply by 22.

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 11 : 9.
(b) Divide ₹8000 in this ratio.
Answer:
(a) Total parts = 11 + 9 = 20.
(b) Value of 1 part = ₹8000 ÷ 20 = ₹400.
First share = 11 × ₹400 = ₹4400.
Second share = 9 × ₹400 = ₹3600.
Check: ₹4400 + ₹3600 = ₹8000.
In simple words: Split ₹8000 into 20 equal parts and give 11 parts to the first and 9 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 cyclist covers 96 km in 6 hours. Find speed.
(b) Distance covered in 11 hours.
Answer:
(a) Speed = distance ÷ time = 96 km ÷ 6 h = 16 km/h.
(b) At the same speed, distance in 11 hours = 16 × 11 = 176 km.
Check: 96 : 6 :: 176 : 11.
In simple words: The cyclist goes 16 km every hour, so in 11 hours it goes 176 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 72 : 108
(b) Simplify 20 : 30
(c) Check whether the two ratios are proportional
Answer:
(a) HCF of 72 and 108 is 36. 72 : 108 = (72 ÷ 36) : (108 ÷ 36) = 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: 72 : 108 :: 20 : 30.
Cross-check: 72 × 30 = 2160 and 108 × 20 = 2160.
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 7 : 5
(b) Quantity of first part if total = 144 mL
(c) Quantity of second part
Answer:
(a) Total parts = 7 + 5 = 12.
(b) 1 part = 144 mL ÷ 12 = 12 mL. First part = 7 × 12 = 84 mL.
(c) Second part = 5 × 12 = 60 mL (or 144 − 84 = 60 mL).
Check: 84 : 60 = 7 : 5.
In simple words: Cut 144 mL into 12 equal parts of 12 mL; the first gets 7 parts and the second 5 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 600 items in 12 hours. Rate per hour
(b) Items produced in 5 hours
(c) Time required to produce 900 items
Answer:
(a) Rate = 600 ÷ 12 = 50 items per hour.
(b) In 5 hours: 50 × 5 = 250 items.
(c) Time = 900 ÷ 50 = 18 hours.
Check: 600 : 12 :: 900 : 18, since 600 × 18 = 12 × 900 = 10800.
In simple words: The machine makes 50 items each hour; multiply by hours to get items, divide items by 50 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 printing press prints 840 pages in 7 hours.
(a) Pages printed per hour
(b) Pages printed in 3 hours
(c) Pages printed in 14 hours
(d) Time required to print 1260 pages
(e) Method used
Answer:
(a) Pages printed per hour = 840 ÷ 7 = 120 pages.
(b) In 3 hours = 120 × 3 = 360 pages.
(c) In 14 hours = 120 × 14 = 1680 pages.
(d) Time = 1260 ÷ 120 = 10.5 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, 7 : 840 :: 10.5 : 1260.
In simple words: The press prints 120 pages an hour; 3 hours give 360 pages, 14 hours give 1680 pages, and 1260 pages take 10.5 hours.

Teacher's Note:
1. A time can be a decimal: 10.5 hours is 10 hours 30 minutes.
2. 14 hours is twice 7 hours, so the pages double: 2 × 840 = 1680, a quick check of part (c).

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

Question 19. Case Study 1: Relief Camp Food Supply
At a relief camp, 300 people are provided food using 45 kg of rice per day. Due to sudden arrival of more families, the number of people increases to 420. To maintain equal food distribution per person, the camp coordinator calculates the quantity of rice required using proportional reasoning.
Answer the following questions:
(a) Rice per person
(b) Write the proportion
(c) Rice required for 420 people
(d) Additional rice required
Answer:
(a) Rice per person = 45 kg ÷ 300 = \( \frac{3}{20} \) kg = 0.15 kg (150 g) per day.
(b) People : rice stays the same, so 300 : 45 :: 420 : x, where x kg is needed for 420 people.
(c) x = \( \frac{45 × 420}{300} \) = 63 kg (or 420 × 0.15 = 63 kg).
(d) Additional rice = 63 − 45 = 18 kg.
Check: 120 more people × 0.15 kg = 18 kg.
In simple words: Each person gets 0.15 kg a day, so 420 people need 63 kg, which is 18 kg more.

Teacher's Note:
1. Equal food per person makes rice directly proportional to the number of people.
2. The extra rice depends only on the extra people: 120 × 0.15 = 18 kg.

Question 20. Case Study 2: Brick Laying Work
A construction worker lays 900 bricks to build a wall of length 15 m. For extending the wall to 24 m with the same height and thickness, the worker calculates the number of bricks required using proportional reasoning to ensure uniform construction.
Answer the following questions:
(a) Bricks used per metre
(b) Write the proportion
(c) Bricks required for 24 m
(d) Extra bricks required
Answer:
(a) Bricks per metre = 900 ÷ 15 = 60 bricks.
(b) Length : bricks stays the same, so 15 : 900 :: 24 : x, where x bricks are needed for 24 m.
(c) x = \( \frac{900 × 24}{15} \) = 1440 bricks (or 24 × 60 = 1440).
(d) Extra bricks = 1440 − 900 = 540 bricks.
In simple words: Each metre of wall takes 60 bricks, so 24 m takes 1440 bricks, which is 540 more.

Teacher's Note:
1. Same height and thickness means bricks are directly proportional to the wall's length.
2. Check (d) another way: 9 extra metres × 60 = 540 bricks.