Proportional Reasoning-1 — Hard

Q1. Read the two statements about image B (width 80 mm, height 60 mm) compared with image A (width 60 mm, height 40 mm). Statement I: B is proportional to A because both height and width of B are 20 mm more than A. Statement II: B is not proportional to A because 80 : 60 = 4 : 3 but 60 : 40 = 3 : 2. Which is correct?

• A. Statement I only
• B. Statement II only
• C. Both I and II
• D. Neither I nor II

Q2. Image E has width 60 mm and height 60 mm. Akash writes the ratio of width to height of image E and also of image A (60 mm × 40 mm) in simplest form. Which pair is correct?

• A. E: 1 : 1, A: 3 : 2
• B. E: 60 : 60, A: 60 : 40
• C. E: 1 : 0, A: 2 : 3
• D. E: 6 : 6, A: 6 : 4

Q3. Reena needs to decide whether 21 : 6 :: 35 : 10 is a true proportion. She reduces each ratio using its HCF. Which conclusion is correct?

• A. 21 : 6 simplifies to 7 : 2; 35 : 10 simplifies to 7 : 2; the proportion is true.
• B. 21 : 6 simplifies to 3 : 1; 35 : 10 simplifies to 7 : 2; the proportion is false.
• C. 21 : 6 simplifies to 7 : 3; 35 : 10 simplifies to 5 : 2; the proportion is false.
• D. 21 : 6 cannot be simplified; the proportion is false.

Q4. A Himachal farmer sells 200 g of tea for ₹200. A Meghalaya estate sells 1 kg of tea for ₹800. Which conclusion about the weight-to-price ratios is correct?

• A. Both simplify to 1 : 1, so the ratios are proportional.
• B. Himachal is 1 : 1; Meghalaya is 5 : 4; the ratios are not proportional.
• C. Himachal is 200 : 200; Meghalaya is 1 : 800; the ratios are proportional.
• D. Himachal is 200 : 1; Meghalaya is 1 : 800; both forms are equivalent.

Q5. Find the missing first term in ____ : 9 :: 14 : 21 so that the ratios are proportional.

• A. 3
• B. 21
• C. 12
• D. 6

Q6. Which of the following sets of ratios are all proportional to 4 : 9? I. 8 : 18 II. 12 : 27 III. 16 : 27 IV. 20 : 45

• A. I, II and IV only
• B. I, III and IV only
• C. II, III and IV only
• D. All four

Q7. Read the statements about the Trairasika method. Statement A: The Sanskrit name Trairasika reflects that the rule uses three known quantities to find a fourth. Statement B: In the rule, the unknown ichchhaphala equals (phala × ichchha) ÷ pramana. Which of the following holds?

• A. Both A and B are true and B explains the formula referred to in A.
• B. Both A and B are true but B does not explain A.
• C. A is true, B is false.
• D. A is false, B is true.

Q8. Using the Rule of Three: a Lilavati problem says 2½ palas of saffron cost 3/7 niskas. How many palas of saffron can be bought for 9 niskas?

• A. 30 palas
• B. 52½ palas
• C. 10½ palas
• D. 21 palas

Q9. A tap takes 15 seconds to fill a mug of 500 mL. Using the Rule of Three, how long will the same tap take to fill a bucket of 10 litres?

• A. 150 seconds
• B. 300 seconds
• C. 200 seconds
• D. 750 seconds

Q10. A cook makes 15 kg of rice for 120 students. Read the two statements about a day when 80 students come. Statement I: The cook should make 15 × (80/120) = 10 kg of rice. Statement II: The cook should make 15 − (120 − 80)/8 = 10 kg of rice. Which gives a method consistent with the Rule of Three?

• A. Statement I only
• B. Statement II only
• C. Both I and II
• D. Neither I nor II

Q11. ₹4,500 is to be divided between two persons in the ratio 2 : 3. Using the chapter's formula, the first person's share is

• A. ₹2,250
• B. ₹1,500
• C. ₹1,800
• D. ₹2,700

Q12. A 40 kg mixture has sand and cement in the ratio 3 : 1. To make the new ratio of sand to cement 5 : 2 without changing the sand, how much cement must be added?

• A. 5 kg
• B. 1 kg
• C. 12 kg
• D. 2 kg

Q13. A student is asked to share 42 marbles in the ratio 4 : 3. She writes: 'Total parts = 4 × 3 = 12, so each part = 42 / 12 = 3.5; shares are 14 and 10.5.' What is the most likely conceptual error?

• A. She used the product 4 × 3 instead of the sum 4 + 3 to count groups.
• B. She forgot to reduce 4 : 3 to its simplest form.
• C. She used division instead of multiplication.
• D. She did not check that the parts add to 42.

Q14. Puneeth's father rode from Lucknow to Kanpur in 2 hours at 50 km/h. If he now drives at 75 km/h, the chapter notes that this problem 'cannot be modelled as 50 : 2 :: 75 : ___'. Why not?

• A. Because 50 and 75 do not share a simple factor.
• B. Because as speed increases the time of travel decreases, not increases.
• C. Because the distance from Lucknow to Kanpur is unknown.
• D. Because the Rule of Three only works for whole numbers.

Q15. Asha collects shampoo prices: sachet 6 mL at ₹2, small bottle 180 mL at ₹154. Volumes are in ratio 6 : 180 = 1 : 30 but prices are 2 : 154 = 1 : 77. The chapter wants the teacher to use this contrast to

• A. Show that bigger bottles always cost less per millilitre.
• B. Help students see that not all real-world quantity-pairs are proportional, and discuss why.
• C. Practise long division of 154 by 2.
• D. Tell students which company is cheating.