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Class 8 Maths: Proportional Reasoning-2, 8 practice questions with answers

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These are 8 practice questions on Chapter 3, Proportional Reasoning-2, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover finding a map's scale and using it, pouring two batches of a four-colour mix together, shares found from the difference between two of them, pie charts for two classes of different sizes, a pie-chart slice when the whole grows, a price rise against a fixed budget, why the number of tiles does not follow the side of a tile, and finding how long one person takes from the time two take together. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-worked by a test script and each question was compared with the chapter's examples, activities and exercises, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 2, Chapter 3, printed pages 55 to 69):

Ratios, maps and sharing

Question 1. (a) Two towns are 150 km apart on the ground and 5 cm apart on a map. Write the map's scale as an RF. (b) On the same map, how far apart should two places 210 km apart be drawn? (c) Aman says that the road between two towns will measure the same on the map as the straight line between them. Is he right?

Answer: (a) 1 : 30,00,000; (b) 7 cm; (c) no. (a) 150 km = 150 × 1,00,000 = 1,50,00,000 cm. So 5 cm on the map stands for 1,50,00,000 cm, and 1 cm stands for 1,50,00,000 ÷ 5 = 30,00,000 cm: the RF is 1 : 30,00,000. (b) 210 km = 2,10,00,000 cm, and 2,10,00,000 ÷ 30,00,000 = 7 cm. (c) An RF gives the geographical (straight-line) distance, not the road distance, and a road bends, so it is longer than the straight line. (Representative fraction, page 56.)

Question 2. A dye-maker has a batch of four colours mixed 6 : 4 : 2 : 1 and pours in a second batch. (a) Explain why, if the second batch is also mixed 6 : 4 : 2 : 1 (in any amount), the combined mix stays 6 : 4 : 2 : 1. (b) Show that if the second batch is mixed 15 : 10 : 5 : 2, then however much of it is poured in, the combined mix can never be 6 : 4 : 2 : 1.

Answer: (a) every colour is multiplied by the same total; (b) it would force the second batch to be zero. (a) Say the first batch is 6k, 4k, 2k, k and the second is 6m, 4m, 2m, m. Together they are 6(k + m), 4(k + m), 2(k + m) and (k + m): the same four numbers times k + m, so the ratio is still 6 : 4 : 2 : 1. (b) Say the second batch is 15m, 10m, 5m, 2m. The combined first and last colours are 6k + 15m and k + 2m. For 6 : 4 : 2 : 1 the first must be 6 times the last: 6k + 15m = 6(k + 2m) = 6k + 12m, so 15m = 12m and m = 0. So any real amount of the second batch changes the mix. (Proportional ratios with more than two terms, page 58.)

Question 3. Ravi, Sita and Tara share some money in the ratio 4 : 5 : 9. Tara gets ₹2,000 more than Ravi. How much does each get, and what is the total?

Answer: Ravi ₹1,600, Sita ₹2,000, Tara ₹3,600; total ₹7,200. Tara's 9 parts and Ravi's 4 parts differ by 9 − 4 = 5 parts, and that difference is ₹2,000, so one part is 2,000 ÷ 5 = ₹400. Then Ravi gets 4 × 400 = ₹1,600, Sita 5 × 400 = ₹2,000 and Tara 9 × 400 = ₹3,600. The total is 18 parts, 18 × 400 = ₹7,200. Check: 3,600 − 1,600 = 2,000. (Ratios with more than two terms, pages 57 to 59.)

Pie charts

Question 4. Two classes, one of 30 children and one of 45, each draw a pie chart of their favourite fruit, and the two charts have exactly the same angles: 144°, 120°, 72° and 24°. Must each slice stand for the same number of children in both classes? Find the numbers.

Answer: no; class of 30: 12, 10, 6 and 2; class of 45: 18, 15, 9 and 3. A slice's angle is proportional to its share of the whole class, not to the number of children itself. In the class of 30, each child is 360° ÷ 30 = 12°, so the slices stand for 144 ÷ 12 = 12, 120 ÷ 12 = 10, 72 ÷ 12 = 6 and 24 ÷ 12 = 2 children. In the class of 45, each child is 360° ÷ 45 = 8°, giving 18, 15, 9 and 3. The same angles mean the same fractions (12/30 = 18/45 = 2/5 for the first fruit), but different numbers. (The angle of a slice is proportional to its quantity, pages 60 and 61.)

Question 5. A school's budget of ₹7,20,000 is shown on a pie chart, and the sports slice is 30°. Next year the budget rises by 20%, but the money for sports stays the same. What is the angle of the sports slice on next year's chart?

Answer: 25°. This year 1° stands for 7,20,000 ÷ 360 = ₹2,000, so sports gets 30 × 2,000 = ₹60,000. Next year the budget is 7,20,000 × 1.2 = ₹8,64,000, and 1° stands for 8,64,000 ÷ 360 = ₹2,400. The same ₹60,000 is now 60,000 ÷ 2,400 = 25°. (The angle shrinks because the same amount is a smaller share of a larger whole: 30 ÷ 1.2 = 25.) (The angle of a slice is proportional to its quantity, page 61.)

Inverse proportion

Question 6. A family spends a fixed ₹600 on rice every month. The price of rice rises from ₹40 a kg to ₹50 a kg, a rise of 25%. By what percentage does the amount of rice they can buy fall?

Answer: by 20%. With a fixed amount of money, the price per kg and the quantity bought are in inverse proportion, since price × quantity is always ₹600. At ₹40 a kg they buy 600 ÷ 40 = 15 kg; at ₹50 a kg they buy 600 ÷ 50 = 12 kg. The fall is 3 kg out of 15, which is 20%. In general, if one quantity is multiplied by n, the other is multiplied by 1/n: here n = 1.25 and 1/1.25 = 0.8, so the quantity becomes 80% of what it was. (Inverse proportion and the factors n and 1/n, pages 64 and 65.)

Question 7. A hall floor is covered by 750 square tiles, each of side 40 cm. Sunil says that with tiles of half the side, 20 cm, you need double the tiles, 1,500. Check this by finding the area, and say which quantity the number of tiles is inversely proportional to.

Answer: 3,000 tiles, four times as many; the number of tiles is inversely proportional to the area of a tile, not to its side. The floor has area 750 × 40 × 40 = 12,00,000 cm². A tile of side 20 cm has area 20 × 20 = 400 cm², so 12,00,000 ÷ 400 = 3,000 tiles. Halving the side makes the area ¼ of what it was, so by the chapter's rule (if one quantity is multiplied by n, the other is multiplied by 1/n) the number of tiles becomes 4 times as many: 750 × 4 = 3,000. Check with the product of area and number: 1,600 × 750 = 12,00,000 and 400 × 3,000 = 12,00,000, the same constant. Sunil used the side, but the product side × number of tiles is not constant (40 × 750 = 30,000, but 20 × 3,000 = 60,000), so the side and the number of tiles are not in inverse proportion. (xy = k, page 64; factors n and 1/n, page 65.)

Question 8. Ria can type a report in 4 hours. Ria and Kabir typing together finish it in 2.4 hours. How long would Kabir take to type the report alone? Check your answer.

Answer: 6 hours. Count the report as 1 unit of work. Ria does 1/4 of it in an hour. Together they do 1 ÷ 2.4 = 5/12 of it in an hour, because the work done and the time taken are directly proportional. So Kabir does 5/12 − 1/4 = 5/12 − 3/12 = 2/12 = 1/6 of it in an hour, and the whole report takes him 1 ÷ (1/6) = 6 hours. Check: in one hour Ria does 1/4 and Kabir 1/6, together 3/12 + 2/12 = 5/12, and 1 ÷ 5/12 = 12/5 = 2.4 hours. (Work done in one hour, and direct proportion of work and time, pages 66 and 67.)

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Sources

All opened and read on 30 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 54.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Proportional Reasoning-2, Class 8 worksheet. Printable, in English, Hindi and Marathi, with an answer key.