Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 105 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹384 (b) ₹312 (c) ₹240 (d) ₹48
2. 2.If 3 mangoes cost ₹51, how much do 5 mangoes cost? (a) ₹255 (b) ₹53 (c) ₹85 (d) ₹102
3. 3.₹90 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹75 (d) ₹45
4. 4.If 3 kites cost ₹24, how much do 4 kites cost? (a) ₹96 (b) ₹40 (c) ₹32 (d) ₹25
5. 5.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 11 days (d) 3 days
6. 6.If 7 kites cost ₹175, how much do 4 kites cost? (a) ₹172 (b) ₹700 (c) ₹125 (d) ₹100
7. 7.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 8 days (d) 10 days
8. 8.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹315 (d) ₹271
9. 9.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 14 days (d) 22 days
10. 10.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹176 (c) ₹132 (d) ₹44
11. 11.If 8 notebooks cost ₹96, how much do 9 notebooks cost? (a) ₹97 (b) ₹108 (c) ₹120 (d) ₹864
12. 12.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹128 (b) ₹16 (c) ₹104 (d) ₹80
13. 13.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 14 days
14. 14.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 7 days
15. 15.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹5 (c) ₹41 (d) ₹40
16. 16.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹312 (d) ₹39
17. 17.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 1 day
18. 18.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 9 days (d) 5 days
19. 19.If 6 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹36 (b) ₹51 (c) ₹27 (d) ₹162
20. 20.3 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 16 days (d) 4 days
21. 21.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹28 (c) ₹56 (d) ₹42
22. 22.If 6 mangoes cost ₹30, how much do 9 mangoes cost? (a) ₹45 (b) ₹270 (c) ₹33 (d) ₹50
23. 23.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹90 (b) ₹15 (c) ₹75 (d) ₹105
24. 24.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹28 (b) ₹126 (c) ₹14 (d) ₹77
25. 25.If 6 notebooks cost ₹90, how much do 10 notebooks cost? (a) ₹150 (b) ₹165 (c) ₹94 (d) ₹900
26. 26.If 9 mangoes cost ₹63, how much do 2 mangoes cost? (a) ₹126 (b) ₹14 (c) ₹21 (d) ₹56
27. 27.If 2 pens cost ₹14, how much do 5 pens cost? (a) ₹35 (b) ₹70 (c) ₹17 (d) ₹42
28. 28.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹126 (d) ₹98
29. 29.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 17 days (c) 16 days (d) 4 days
30. 30.If 6 notebooks cost ₹96, how much do 10 notebooks cost? (a) ₹160 (b) ₹176 (c) ₹100 (d) ₹960
31. 31.If 8 pens cost ₹24, how much do 3 pens cost? (a) ₹12 (b) ₹9 (c) ₹19 (d) ₹72
32. 32.If 7 kites cost ₹105, how much do 2 kites cost? (a) ₹45 (b) ₹30 (c) ₹100 (d) ₹210
33. 33.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹116 (b) ₹58 (c) ₹29 (d) ₹87
34. 34.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹252 (b) ₹36 (c) ₹180 (d) ₹216
35. 35.₹207 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹207 (b) ₹185 (c) ₹184 (d) ₹23
36. 36.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹10 (d) ₹30
37. 37.If 7 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹44 (b) ₹40 (c) ₹280 (d) ₹31
38. 38.If 4 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹36 (b) ₹35 (c) ₹108 (d) ₹27
39. 39.₹264 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹231 (b) ₹132 (c) ₹264 (d) ₹33
40. 40.If 6 mangoes cost ₹144, how much do 4 mangoes cost? (a) ₹142 (b) ₹96 (c) ₹576 (d) ₹120

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