Chapter: Proportional Reasoning-1 (NCERT Ganita Prakash)
1. The ratio of width to height of Image A is 60 : 40. Its simplest form is
(a) 2 : 3 (b) 3 : 2 (c) 4 : 3 (d) 3 : 4
2. Which of the following ratios is already in its simplest form?
(a) 18 : 24 (b) 72 : 96 (c) 14 : 21 (d) 5 : 170
3. If 6 : 10 :: 18 : x, then the value of x is
(a) 20 (b) 25 (c) 30 (d) 36
4. Two ratios a : b and c : d are proportional if
(a) a + b = c + d (b) ad = bc (c) ac = bd (d) a – b = c – d
5. The HCF of 90 and 60 is 30. The simplest form of 90 : 60 is
(a) 2 : 3 (b) 3 : 2 (c) 9 : 6 (d) 15 : 10
6. Assertion (A): 60 : 40 and 90 : 60 are proportional.
Reason (R): Both ratios reduce to the same simplest form 3 : 2.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
7. Assertion (A): When the same number is added to both terms of a ratio, the new ratio remains proportional to the original ratio.
Reason (R): Adding the same number changes the terms by the same additive difference, not by the same multiplicative factor.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
8. In the Rule of Three, if pramāṇa = a, phala = b and ichchhā = c, then ichchhāphala is given by
(a) (b × c) ÷ a (b) (a × c) ÷ b (c) (a × b) ÷ c (d) a + b + c
9. The ratio of grey bricks to coloured bricks in pattern (a) of the brick wall is 9 : 6. Its simplest form is
(a) 2 : 3 (b) 3 : 2 (c) 9 : 6 (d) 6 : 9
10. If a quantity x is to be divided in the ratio m : n, the two parts are
(a) m × x/(m + n) and n × x/(m + n)
(b) m × x and n × x
(c) (m + n) × x and x
(d) m/(m + n) and n/(m + n)
11. Reduce the ratio 72 : 96 to its simplest form.
12. Are the ratios 4 : 7 and 12 : 21 proportional? Give reason.
13. If 14 : 21 :: ? : 42, find the missing term.
14. State the condition ad = bc in words for two ratios a : b and c : d to be proportional.
15. Write the ratio of teachers to students 5 : 170 in its simplest form.
16. When Neelima is 3 years old, the ratio of her age to her mother’s age is 1 : 10. What is the simplest form of this ratio?
17. Fill in the missing terms so that the ratios are proportional to 18 : 24:
3 : ___ , 12 : ___ , 20 : ___ , 27 : ___
18. A car travels 90 km in 150 minutes. Using cross-multiplication, find the distance it will travel in 240 minutes.
19. Divide ₹4500 in the ratio 2 : 3. Show the two parts obtained.
20. In a mixture of 40 kg, sand and cement are in the ratio 3 : 1. Find the quantity of sand and cement.
21. Check whether 21 : 6 and 35 : 10 are proportional by reducing both to simplest form.
22. Kesang made 6 glasses of lemonade with 10 spoons of sugar. She now wants to make 18 more glasses while keeping the same sweetness. How many spoons of sugar should she add? Show the proportion and the factor of change.
23. Prashanti invested ₹75 000 and Bhuvan invested ₹25 000 in a food-cart business. They earned a profit of ₹4000 in the first month and decided to share it in the ratio of their investments. Find each person’s share. Also explain why the ratios of investment and profit share are proportional.
24. A small farmer sells 200 g tea packets for ₹200 while a large estate sells 1 kg packets for ₹800. Are the weight-to-price ratios proportional? Which tea is more expensive per kg? Justify your answer with complete calculations (convert units where necessary).
25. Case: Scaling a Filter-Coffee Recipe
Manjunath mixes 15 mL coffee decoction with 35 mL milk for regular filter coffee (ratio 15 : 35). For stronger coffee he uses 20 mL decoction and 30 mL milk. For lighter coffee he uses 10 mL decoction and 40 mL milk.
(a) Reduce the regular ratio 15 : 35 to simplest form. (1)
(b) Reduce the stronger ratio 20 : 30 to simplest form and state whether it is proportional to the regular ratio. (1)
(c) Reduce the lighter ratio 10 : 40 to simplest form and state whether it is proportional to the regular ratio. (1)
(d) If Manjunath wants to make 5 cups of regular coffee, how much decoction and milk will he need? (1)
26. Case: Brick-Wall Pattern
A long brick wall is built using a repeating pattern of grey and coloured bricks. In one block of the pattern there are 9 grey bricks and 6 coloured bricks. The same pattern continues throughout the wall.
(a) Write the ratio of grey bricks to coloured bricks in simplest form. (1)
(b) If the mason builds a 30-block section of the wall, how many grey bricks will be used? (1)
(c) How many coloured bricks will be used in the same 30-block section? (1)
(d) If another pattern uses grey and coloured bricks in the ratio 4 : 3, is this ratio proportional to 3 : 2? Give reason. (1)
1. (b) 3 : 2 (1 mark)
2. (d) 5 : 170 (1 mark)
3. (c) 30 (1 mark)
4. (b) ad = bc (1 mark)
5. (b) 3 : 2 (1 mark)
6. (a) (1 mark)
7. (d) (1 mark)
8. (a) (1 mark)
9. (b) (1 mark)
10. (a) (1 mark)
11. HCF of 72 and 96 is 24.
72 ÷ 24 = 3, 96 ÷ 24 = 4 → 3 : 4 (2 marks)
12. Both reduce to 4 : 7 (HCF of 12 & 21 = 3). Hence proportional. (2 marks)
13. 14 : 21 :: 28 : 42 (multiply both terms by 2). (2 marks)
14. Two ratios a : b and c : d are proportional when the product of the extremes equals the product of the means (ad = bc). (2 marks)
15. HCF of 5 and 170 is 5 → 1 : 34. (2 marks)
16. 3 : 30 reduces to 1 : 10. (2 marks)
17. 3 : 4, 12 : 16, 20 : 26⅔ (or 60 : 80), 27 : 36 (1 mark each, total 3)
18. 150 : 90 :: 240 : x
150x = 240 × 90 → x = 144 km (cross-multiplication 2 marks, answer 1 mark)
19. Total parts = 5. Each part = ₹900.
Parts: ₹1800 and ₹2700. (3 marks)
20. Sand = 3/4 × 40 = 30 kg, Cement = 1/4 × 40 = 10 kg. (3 marks)
21. 21 : 6 → 7 : 2; 35 : 10 → 7 : 2. Same simplest form → proportional. (3 marks)
22. 6 : 10 :: 18 : x. Factor = 18/6 = 3.
x = 10 × 3 = 30 spoons. (5 marks: proportion 2, factor 1, calculation 2)
23. Ratio 75 000 : 25 000 = 3 : 1. Total parts = 4.
Prashanti = 3 × 1000 = ₹3000; Bhuvan = ₹1000.
Both investment and profit ratios reduce to 3 : 1 → proportional. (5 marks)
24. Himachal: 200 g : ₹200 → 1 : 1 (simplest).
Meghalaya: 1000 g : ₹800 → 5 : 4 (simplest). Not proportional.
Cost per kg: Himachal ₹1000, Meghalaya ₹800 → Himachal more expensive. (5 marks)
25. (a) 3 : 7 (1)
(b) 2 : 3 – not proportional to 3 : 7 (1)
(c) 1 : 4 – not proportional to 3 : 7 (1)
(d) Decoction 75 mL, milk 175 mL (1)
26. (a) 3 : 2 (1)
(b) 270 grey bricks (1)
(c) 180 coloured bricks (1)
(d) 4 : 3 ≠ 3 : 2 → not proportional (1)
All questions are answerable from the NCERT chapter text. Reviewed by GFIS faculty.