Set A Solutions

A1. Answer: (a) 3 : 4 HCF of 45 and 60 is 15. 45÷15 : 60÷15 = 3 : 4.

A2. Answer: (a) 8 : 3 2 hours = 120 minutes. 120 : 45 → divide by 15 → 8 : 3.

A3. Answer: (a) 8 : 12 : 15 LCM of b-terms (3, 4) = 12. a:b = 2:3 = 8:12. b:c = 4:5 = 12:15. So a:b:c = 8:12:15.

A4. Answer: (b) ₹240 Total parts = 2+3+4 = 9. Value of 1 part = 720/9 = 80. B’s share = 3 × 80 = 240.

A5. Answer: (a) 1 : 2 Compound ratio = (2×3):(3×4) = 6:12 = 1:2.

A6. Answer: (a) 25 : 36 Duplicate ratio of a:b is a²:b². 5²:6² = 25:36.

A7. Answer: (a) 4 : 5 Sub-duplicate ratio of a:b is √a : √b. √16:√25 = 4:5.

A8. Answer: (a) 15 Mean proportional = √(9×25) = √225 = 15.

A9. Answer: (a) 12 Third proportional to a, b = b²/a = 6²/3 = 36/3 = 12.

A10. Answer: (a) 15 Fourth proportional to a,b,c = bc/a = (5×9)/3 = 45/3 = 15.

A11. Answer: (a) 80, 100 Total parts = 4+5 = 9. 1 part = 180/9 = 20. Numbers = 4×20=80, 5×20=100.

A12. Answer: (a) 18 : 25 Let x=3, y=4 (using the ratio directly). 2x+3y = 6+12 = 18. 3x+4y = 9+16 = 25. Ratio = 18:25.

A13. Answer: (a) 35 5 parts = 25 years → 1 part = 5 years. B = 7 parts = 7×5 = 35 years.

A14. Answer: (a) 4 a=5, b=3 (from ratio 5:3). (a+b)/(a−b) = 8/2 = 4.

A15. Answer: (a) 21 2 parts = 14 → 1 part = 7. Second term = 3×7 = 21.

A16. Answer: (b) 1 : 3 Compound ratio = (3×5) : (5×9) = 15 : 45. Divide both terms by 15: 1 : 3.

A17. Answer: (a) 20 Third proportional to a, b = b²/a = 10²/5 = 100/5 = 20.

A18. Answer: (c) ₹400 Total parts = 5+7 = 12. Value of 1 part = 960/12 = 80. A’s share = 5 × 80 = ₹400.

A19. Answer: (d) 2 : 3 Convert to decimals: 2/3 = 0.667, 3/5 = 0.6, 5/8 = 0.625. The largest value is 0.667, so 2 : 3 is the greatest.

A20. Answer: (a) 24 5 parts = 30 years → 1 part = 6 years. P = 4 parts = 4×6 = 24 years.