Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 83 · 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.If 6 pens cost ₹72, how much do 2 pens cost? (a) ₹144 (b) ₹36 (c) ₹68 (d) ₹24
2. 2.If 6 pens cost ₹150, how much do 11 pens cost? (a) ₹275 (b) ₹155 (c) ₹1650 (d) ₹300
3. 3.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹209 (b) ₹38 (c) ₹152 (d) ₹266
4. 4.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹114 (d) ₹95
5. 5.If 7 notebooks cost ₹119, how much do 2 notebooks cost? (a) ₹51 (b) ₹238 (c) ₹114 (d) ₹34
6. 6.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹234 (d) ₹195
7. 7.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹91 (b) ₹78 (c) ₹65 (d) ₹13
8. 8.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹69 (b) ₹23 (c) ₹115 (d) ₹92
9. 9.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹132 (b) ₹22 (c) ₹66 (d) ₹110
10. 10.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹63 (b) ₹54 (c) ₹45 (d) ₹9
11. 11.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹57 (d) ₹95
12. 12.₹414 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹207 (b) ₹368 (c) ₹414 (d) ₹46
13. 13.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 25 days (c) 5 days (d) 4 days
14. 14.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹392 (b) ₹393 (c) ₹49 (d) ₹441
15. 15.If 9 kites cost ₹225, how much do 3 kites cost? (a) ₹100 (b) ₹219 (c) ₹675 (d) ₹75
16. 16.If 7 pens cost ₹49, how much do 12 pens cost? (a) ₹54 (b) ₹91 (c) ₹588 (d) ₹84
17. 17.If 4 mangoes cost ₹44, how much do 8 mangoes cost? (a) ₹352 (b) ₹48 (c) ₹99 (d) ₹88
18. 18.If 2 kites cost ₹10, how much do 7 kites cost? (a) ₹70 (b) ₹40 (c) ₹35 (d) ₹15
19. 19.If 4 pens cost ₹96, how much do 3 pens cost? (a) ₹96 (b) ₹288 (c) ₹72 (d) ₹95
20. 20.If 4 notebooks cost ₹76, how much do 10 notebooks cost? (a) ₹82 (b) ₹209 (c) ₹760 (d) ₹190
21. 21.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 13 days (d) 10 days
22. 22.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 4 days (d) 6 days
23. 23.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹13 (c) ₹65 (d) ₹117
24. 24.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹10 (c) ₹45 (d) ₹80
25. 25.If 3 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹56 (b) ₹70 (c) ₹43 (d) ₹168
26. 26.If 8 pens cost ₹128, how much do 4 pens cost? (a) ₹80 (b) ₹124 (c) ₹64 (d) ₹512
27. 27.If 3 kites cost ₹12, how much do 12 kites cost? (a) ₹21 (b) ₹144 (c) ₹52 (d) ₹48
28. 28.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 1 day
29. 29.If 4 pens cost ₹72, how much do 2 pens cost? (a) ₹144 (b) ₹70 (c) ₹36 (d) ₹54
30. 30.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹126 (b) ₹42 (c) ₹63 (d) ₹84
31. 31.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹40 (c) ₹48 (d) ₹8
32. 32.If 6 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹59 (b) ₹594 (c) ₹99 (d) ₹108
33. 33.₹322 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹276 (b) ₹161 (c) ₹46 (d) ₹322
34. 34.If 2 mangoes cost ₹18, how much do 5 mangoes cost? (a) ₹21 (b) ₹54 (c) ₹90 (d) ₹45
35. 35.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹93 (b) ₹62 (c) ₹124 (d) ₹31
36. 36.If 3 kites cost ₹63, how much do 11 kites cost? (a) ₹231 (b) ₹252 (c) ₹693 (d) ₹71
37. 37.If 9 pens cost ₹144, how much do 10 pens cost? (a) ₹176 (b) ₹160 (c) ₹1440 (d) ₹145
38. 38.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 2 days (d) 3 days
39. 39.If 5 mangoes cost ₹45, how much do 2 mangoes cost? (a) ₹27 (b) ₹90 (c) ₹42 (d) ₹18
40. 40.If 4 kites cost ₹100, how much do 7 kites cost? (a) ₹200 (b) ₹103 (c) ₹700 (d) ₹175

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