10. Practice Question Set A — Basic Level (20 MCQs)

This set tests the direct application of definitions and formulas covered in Sections 2 to 6 — ratio simplification, unit conversion, continued ratio, dividing a sum, compound/duplicate/sub-duplicate ratios, mean/third/fourth proportional, and a first taste of componendo-dividendo and age ratios. Attempt every question without a calculator; each is designed to be solvable within 30–40 seconds using the shortcuts from Section 8.

A1. [Simplification] Simplify the ratio 45 : 60. (a) 3 : 4 (b) 4 : 5 (c) 2 : 3 (d) 5 : 6

A2. [Unit Conversion] Find the ratio of 2 hours to 45 minutes. (a) 8 : 3 (b) 3 : 8 (c) 4 : 3 (d) 5 : 2

A3. [Continued Ratio] If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c. (a) 8 : 12 : 15 (b) 6 : 8 : 15 (c) 2 : 4 : 5 (d) 8 : 10 : 15

A4. [Dividing a Sum] ₹720 is divided among A, B, C in the ratio 2 : 3 : 4. Find B’s share. (a) ₹160 (b) ₹240 (c) ₹320 (d) ₹200

A5. [Compound Ratio] Find the compound ratio of 2 : 3 and 3 : 4. (a) 1 : 2 (b) 2 : 3 (c) 3 : 4 (d) 1 : 4

A6. [Duplicate Ratio] Find the duplicate ratio of 5 : 6. (a) 25 : 36 (b) 10 : 12 (c) 25 : 30 (d) 15 : 18

A7. [Sub-duplicate Ratio] Find the sub-duplicate ratio of 16 : 25. (a) 4 : 5 (b) 8 : 10 (c) 2 : 5 (d) 16 : 5

A8. [Mean Proportional] Find the mean proportional between 9 and 25. (a) 15 (b) 17 (c) 12 (d) 18

A9. [Third Proportional] Find the third proportional to 3 and 6. (a) 12 (b) 9 (c) 18 (d) 15

A10. [Fourth Proportional] Find the fourth proportional to 3, 5, 9. (a) 15 (b) 12 (c) 18 (d) 27

A11. [Dividing a Sum, 2-part] Two numbers are in the ratio 4 : 5. Their sum is 180. Find the numbers. (a) 80, 100 (b) 70, 110 (c) 90, 90 (d) 60, 120

A12. [Ratio Expression] If x : y = 3 : 4, find (2x + 3y) : (3x + 4y). (a) 18 : 25 (b) 6 : 7 (c) 9 : 13 (d) 17 : 24

A13. [Age Ratio] The ages of A and B are in the ratio 5 : 7. If A is 25 years old, find B’s age. (a) 35 (b) 30 (c) 40 (d) 45

A14. [Componendo-Dividendo, Basic] If a/b = 5/3, find the value of (a+b)/(a−b). (a) 4 (b) 2 (c) 8 (d) 15/2

A15. [Ratio Scaling] In the ratio 2 : 3, if the first term is 14, find the second term. (a) 21 (b) 18 (c) 24 (d) 28

A16. [Compound Ratio] Find the compound ratio of 3 : 5 and 5 : 9. (a) 3 : 1 (b) 1 : 3 (c) 5 : 9 (d) 1 : 9

A17. [Third Proportional] Find the third proportional to 5 and 10. (a) 20 (b) 15 (c) 25 (d) 10

A18. [Dividing a Sum] ₹960 is divided between A and B in the ratio 5 : 7. Find A’s share. (a) ₹480 (b) ₹560 (c) ₹400 (d) ₹320

A19. [Ratio Comparison] Which of the following ratios is the greatest — 2 : 3, 3 : 5, or 5 : 8? (a) 3 : 5 (b) 5 : 8 (c) All are equal (d) 2 : 3

A20. [Age Ratio] The present ages of P and Q are in the ratio 4 : 5. If Q is 30 years old, find P’s age. (a) 24 (b) 20 (c) 28 (d) 32