Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 52 · 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 3 kites cost ₹54, how much do 12 kites cost? (a) ₹234 (b) ₹216 (c) ₹648 (d) ₹63
2. 2.If 8 mangoes cost ₹176, how much do 9 mangoes cost? (a) ₹177 (b) ₹220 (c) ₹1584 (d) ₹198
3. 3.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹35 (b) ₹5 (c) ₹25 (d) ₹15
4. 4.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹96 (b) ₹432 (c) ₹264 (d) ₹48
5. 5.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹172 (b) ₹129 (c) ₹43 (d) ₹215
6. 6.If 6 pens cost ₹126, how much do 3 pens cost? (a) ₹63 (b) ₹84 (c) ₹123 (d) ₹378
7. 7.If 4 mangoes cost ₹48, how much do 5 mangoes cost? (a) ₹60 (b) ₹72 (c) ₹49 (d) ₹240
8. 8.If 5 pens cost ₹55, how much do 6 pens cost? (a) ₹330 (b) ₹66 (c) ₹77 (d) ₹56
9. 9.If 4 mangoes cost ₹88, how much do 9 mangoes cost? (a) ₹198 (b) ₹220 (c) ₹93 (d) ₹792
10. 10.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 12 days (d) 2 days
11. 11.If 7 pens cost ₹105, how much do 10 pens cost? (a) ₹165 (b) ₹1050 (c) ₹108 (d) ₹150
12. 12.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹42 (b) ₹231 (c) ₹84 (d) ₹378
13. 13.If 3 pens cost ₹42, how much do 12 pens cost? (a) ₹182 (b) ₹51 (c) ₹504 (d) ₹168
14. 14.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹312 (b) ₹48 (c) ₹192 (d) ₹432
15. 15.If 8 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹288 (b) ₹33 (c) ₹36 (d) ₹40
16. 16.If 3 kites cost ₹57, how much do 4 kites cost? (a) ₹95 (b) ₹58 (c) ₹228 (d) ₹76
17. 17.If 8 kites cost ₹64, how much do 9 kites cost? (a) ₹576 (b) ₹65 (c) ₹80 (d) ₹72
18. 18.If 5 kites cost ₹80, how much do 11 kites cost? (a) ₹880 (b) ₹176 (c) ₹86 (d) ₹192
19. 19.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹180 (d) ₹162
20. 20.₹182 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹91 (b) ₹26 (c) ₹52 (d) ₹130
21. 21.If 2 notebooks cost ₹22, how much do 11 notebooks cost? (a) ₹31 (b) ₹242 (c) ₹121 (d) ₹132
22. 22.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹115 (b) ₹207 (c) ₹184 (d) ₹23
23. 23.If 6 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹20 (b) ₹27 (c) ₹144 (d) ₹24
24. 24.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 17 days (d) 16 days
25. 25.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 36 days (d) 18 days
26. 26.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹117 (b) ₹156 (c) ₹39 (d) ₹78
27. 27.If 5 notebooks cost ₹125, how much do 4 notebooks cost? (a) ₹124 (b) ₹500 (c) ₹125 (d) ₹100
28. 28.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 27 days (d) 3 days
29. 29.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 21 days (c) 7 days (d) 63 days
30. 30.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 27 days (d) 3 days
31. 31.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹92 (b) ₹46 (c) ₹115 (d) ₹138
32. 32.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 16 days (d) 36 days
33. 33.₹288 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹32 (b) ₹144 (c) ₹256 (d) ₹288
34. 34.If 4 mangoes cost ₹48, how much do 3 mangoes cost? (a) ₹47 (b) ₹48 (c) ₹36 (d) ₹144
35. 35.₹450 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹400 (b) ₹50 (c) ₹450 (d) ₹225
36. 36.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹79 (c) ₹13 (d) ₹78
37. 37.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹105 (b) ₹140 (c) ₹175 (d) ₹35
38. 38.If 6 pens cost ₹42, how much do 7 pens cost? (a) ₹294 (b) ₹56 (c) ₹43 (d) ₹49
39. 39.If 5 pens cost ₹90, how much do 7 pens cost? (a) ₹630 (b) ₹126 (c) ₹144 (d) ₹92
40. 40.If 8 mangoes cost ₹48, how much do 11 mangoes cost? (a) ₹528 (b) ₹72 (c) ₹66 (d) ₹51

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