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Class 8 Maths: Proportional Reasoning-1, 8 practice questions with answers

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These are 8 practice questions on Chapter 7, Proportional Reasoning-1, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 1. Each has a worked answer and the textbook page it comes from. They cover why adding the same amount to both terms of a ratio breaks the proportion, when the rule of three can and cannot be used, working back from one share, a map scale, currency, testing whether fares are proportional, splitting into three parts, and shadows. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, 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 1, Chapter 7, printed pages 159 to 177):

Ratios and the rule of three

Question 1. A rangoli design uses 55 red and 22 yellow flowers. Meena makes a bigger one with 59 red flowers. How many yellow flowers would keep exactly the same colour balance, and can she do it with whole flowers? If a bigger rangoli uses 95 red flowers, how many yellow flowers keep the same ratio?

Answer: 23.6 yellow, so not with whole flowers; 38 yellow for 95 red. The ratio 55 : 22 is 5 : 2 in its simplest form (dividing both terms by their HCF), so the yellow flowers must be 2/5 of the red ones. For 59 red that is 2 × 59 ÷ 5 = 23.6, not a whole number, so no whole number of yellow flowers keeps exactly the same balance with 59 red. (Adding 4 of each, 59 : 26, would not keep it either, because adding the same number to both terms changes a ratio.) For 95 red: 5 : 2 :: 95 : y, so 5y = 2 × 95 = 190 and y = 38. (Ratios in their simplest form, page 161; adding the same number changes a ratio, page 164; cross multiplication, page 168.)

Question 2. Which of these can be solved with the rule of three? Solve the one that can. (a) 6 pens cost ₹246. What do 17 pens cost? (b) 4 painters paint a wall in 9 days. How long would 6 painters take?

Answer: (a) yes, ₹697; (b) no. (a) More pens cost proportionally more: 6 : 246 :: 17 : x, so x = 246 × 17 ÷ 6 = ₹697 (₹41 per pen). (b) More painters finish faster, so the number of days goes down as the number of painters goes up; the ratios are not proportional, and the rule of three does not apply, just like speed and time on the same journey. (Rule of Three, pages 167 to 169; when it does not apply, page 171.)

Question 3. Prize money is shared between two teams in the ratio 5 : 3. The bigger share is ₹1350. Find the smaller share and the total prize.

Answer: smaller share ₹810; total ₹2160. The bigger share is 5 equal groups, so one group is 1350 ÷ 5 = ₹270. The smaller share is 3 groups: 3 × 270 = ₹810. The total is 8 groups: 8 × 270 = ₹2160. (Dividing a quantity in a ratio, pages 173 and 174.)

Proportion in the real world

Question 4. A district map has the scale 1 : 250000, which means 1 cm on the map stands for 250000 cm on the ground. Two villages are 6.6 cm apart on the map. How far apart are they, in km?

Answer: 16.5 km. By proportion, 1 : 250000 :: 6.6 : d, so d = 250000 × 6.6 = 1650000 cm. Since 1 km = 100000 cm, that is 1650000 ÷ 100000 = 16.5 km. (Map scales are not in the chapter; the method is the rule of three, pages 167 to 169, with a unit conversion as in Example 9, page 169.)

Question 5. On a certain day, 3 US dollars could be exchanged for ₹252. At the same rate, how many rupees would 17 dollars give?

Answer: ₹1428. 3 : 252 :: 17 : x, so x = 252 × 17 ÷ 3 = 84 × 17 = ₹1428. (Rule of Three, pages 167 to 169; the exchange rate is an example of our own, not from the chapter.)

Question 6. An auto-rickshaw charged ₹55 for 2.5 km, ₹99 for 4.5 km and ₹124 for 6 km. Are the fares proportional to the distances? If not, which fare breaks the pattern?

Answer: no; the ₹124 fare for 6 km breaks it. 55 : 2.5 and 99 : 4.5 are both 22 : 1 (₹22 per km), so these two are proportional. At ₹22 per km, 6 km would cost 6 × 22 = ₹132, but the fare was ₹124, so 124 : 6 is not 22 : 1. (Checking whether ratios are proportional, pages 161 and 162.)

Question 7. A shop mixes peanuts, raisins and cashews in the ratio 1 : 2 : 4 to make a trail mix. How much of each is in a 2.8 kg packet?

Answer: 0.4 kg peanuts, 0.8 kg raisins and 1.6 kg cashews. The mix has 1 + 2 + 4 = 7 equal groups, so one group is 2.8 ÷ 7 = 0.4 kg. Peanuts are 1 group (0.4 kg), raisins are 2 groups (0.8 kg) and cashews are 4 groups (1.6 kg). Check: 0.4 + 0.8 + 1.6 = 2.8. (Dividing in a ratio, extended from two parts to three, pages 173 and 174.)

Question 8. At the same time of day, a girl 1.6 m tall casts a shadow 2.4 m long, and a building casts a shadow 33 m long. How tall is the building?

Answer: 22 m. At the same time, heights and shadow lengths are proportional: 1.6 : 2.4 :: h : 33. Cross multiplying, 2.4 × h = 1.6 × 33, so h = 52.8 ÷ 2.4 = 22 m. (Cross multiplication, page 168.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 158.

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.