Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 144 · 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.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹57 (d) ₹39
2. 2.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹56 (d) ₹48
3. 3.If 6 pens cost ₹18, how much do 5 pens cost? (a) ₹18 (b) ₹17 (c) ₹15 (d) ₹90
4. 4.If 3 mangoes cost ₹75, how much do 2 mangoes cost? (a) ₹74 (b) ₹150 (c) ₹75 (d) ₹50
5. 5.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹110 (b) ₹80 (c) ₹140 (d) ₹20
6. 6.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 30 days (d) 31 days
7. 7.If 6 kites cost ₹84, how much do 2 kites cost? (a) ₹28 (b) ₹42 (c) ₹168 (d) ₹80
8. 8.If 2 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹60 (b) ₹30 (c) ₹36 (d) ₹15
9. 9.If 6 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹29 (b) ₹264 (c) ₹44 (d) ₹48
10. 10.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹351 (b) ₹390 (c) ₹195 (d) ₹39
11. 11.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹154 (d) ₹198
12. 12.If 9 notebooks cost ₹81, how much do 12 notebooks cost? (a) ₹117 (b) ₹84 (c) ₹108 (d) ₹972
13. 13.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹36 (c) ₹108 (d) ₹72
14. 14.If 3 pens cost ₹57, how much do 4 pens cost? (a) ₹58 (b) ₹228 (c) ₹95 (d) ₹76
15. 15.If 7 mangoes cost ₹84, how much do 6 mangoes cost? (a) ₹83 (b) ₹84 (c) ₹72 (d) ₹504
16. 16.If 2 notebooks cost ₹8, how much do 12 notebooks cost? (a) ₹52 (b) ₹18 (c) ₹48 (d) ₹96
17. 17.If 9 mangoes cost ₹81, how much do 6 mangoes cost? (a) ₹78 (b) ₹54 (c) ₹63 (d) ₹486
18. 18.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹72 (b) ₹90 (c) ₹55 (d) ₹216
19. 19.If 9 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹216 (b) ₹26 (c) ₹27 (d) ₹24
20. 20.If 2 notebooks cost ₹38, how much do 12 notebooks cost? (a) ₹247 (b) ₹48 (c) ₹228 (d) ₹456
21. 21.If 3 kites cost ₹27, how much do 10 kites cost? (a) ₹270 (b) ₹99 (c) ₹90 (d) ₹34
22. 22.If 8 mangoes cost ₹200, how much do 9 mangoes cost? (a) ₹1800 (b) ₹225 (c) ₹250 (d) ₹201
23. 23.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 36 days (c) 4 days (d) 5 days
24. 24.₹264 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹264 (b) ₹220 (c) ₹132 (d) ₹44
25. 25.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹26 (b) ₹104 (c) ₹130 (d) ₹78
26. 26.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹329 (d) ₹282
27. 27.If 8 pens cost ₹96, how much do 2 pens cost? (a) ₹24 (b) ₹36 (c) ₹90 (d) ₹192
28. 28.If 8 notebooks cost ₹48, how much do 12 notebooks cost? (a) ₹576 (b) ₹78 (c) ₹52 (d) ₹72
29. 29.₹192 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹24 (b) ₹96 (c) ₹192 (d) ₹168
30. 30.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹160 (c) ₹128 (d) ₹32
31. 31.If 7 notebooks cost ₹175, how much do 8 notebooks cost? (a) ₹1400 (b) ₹176 (c) ₹225 (d) ₹200
32. 32.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 3 days (d) 4 days
33. 33.If 2 kites cost ₹36, how much do 9 kites cost? (a) ₹43 (b) ₹180 (c) ₹324 (d) ₹162
34. 34.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹132 (b) ₹660 (c) ₹111 (d) ₹154
35. 35.If 7 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹126 (b) ₹18 (c) ₹27 (d) ₹58
36. 36.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹195 (d) ₹117
37. 37.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 23 days (d) 22 days
38. 38.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹70 (b) ₹126 (c) ₹140 (d) ₹14
39. 39.₹84 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹56 (d) ₹84
40. 40.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹16 (b) ₹48 (c) ₹128 (d) ₹88

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