Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 763 · 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. 1.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 4 days (d) 5 days
2. 2.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹64 (d) ₹32
3. 3.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹336 (c) ₹48 (d) ₹240
4. 4.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹182 (d) ₹234
5. 5.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹96 (b) ₹54 (c) ₹12 (d) ₹108
6. 6.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹125 (b) ₹175 (c) ₹150 (d) ₹25
7. 7.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹152 (b) ₹209 (c) ₹266 (d) ₹38
8. 8.If 9 notebooks cost ₹189, how much do 3 notebooks cost? (a) ₹183 (b) ₹84 (c) ₹63 (d) ₹567
9. 9.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹52 (b) ₹13 (c) ₹39 (d) ₹65
10. 10.If 3 mangoes cost ₹45, how much do 7 mangoes cost? (a) ₹49 (b) ₹120 (c) ₹315 (d) ₹105
11. 11.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 32 days (c) 2 days (d) 33 days
12. 12.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 4 days (d) 11 days
13. 13.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹210 (b) ₹168 (c) ₹42 (d) ₹105
14. 14.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 44 days (d) 45 days
15. 15.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹235 (c) ₹47 (d) ₹376
16. 16.If 7 notebooks cost ₹70, how much do 8 notebooks cost? (a) ₹90 (b) ₹80 (c) ₹560 (d) ₹71
17. 17.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 6 days (d) 8 days
18. 18.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 48 days (d) 3 days
19. 19.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹261 (d) ₹203
20. 20.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 5 days (d) 3 days
21. 21.If 3 notebooks cost ₹45, how much do 12 notebooks cost? (a) ₹180 (b) ₹540 (c) ₹54 (d) ₹195
22. 22.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹215 (b) ₹173 (c) ₹43 (d) ₹172
23. 23.If 4 notebooks cost ₹64, how much do 8 notebooks cost? (a) ₹512 (b) ₹128 (c) ₹144 (d) ₹68
24. 24.If 3 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹52 (b) ₹128 (c) ₹336 (d) ₹112
25. 25.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹306 (b) ₹54 (c) ₹102 (d) ₹119
26. 26.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 19 days
27. 27.If 5 notebooks cost ₹115, how much do 8 notebooks cost? (a) ₹920 (b) ₹207 (c) ₹184 (d) ₹118
28. 28.If 4 pens cost ₹84, how much do 8 pens cost? (a) ₹189 (b) ₹672 (c) ₹88 (d) ₹168
29. 29.If 7 mangoes cost ₹126, how much do 6 mangoes cost? (a) ₹756 (b) ₹125 (c) ₹108 (d) ₹126
30. 30.If 3 pens cost ₹42, how much do 12 pens cost? (a) ₹51 (b) ₹504 (c) ₹182 (d) ₹168
31. 31.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 4 days
32. 32.If 8 pens cost ₹104, how much do 11 pens cost? (a) ₹143 (b) ₹107 (c) ₹1144 (d) ₹156
33. 33.If 6 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹44 (b) ₹96 (c) ₹16 (d) ₹24
34. 34.If 8 notebooks cost ₹192, how much do 5 notebooks cost? (a) ₹144 (b) ₹960 (c) ₹120 (d) ₹189
35. 35.If 2 pens cost ₹22, how much do 12 pens cost? (a) ₹32 (b) ₹264 (c) ₹143 (d) ₹132
36. 36.If 6 mangoes cost ₹150, how much do 7 mangoes cost? (a) ₹200 (b) ₹1050 (c) ₹175 (d) ₹151
37. 37.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 9 days (d) 17 days
38. 38.If 6 notebooks cost ₹78, how much do 4 notebooks cost? (a) ₹76 (b) ₹312 (c) ₹52 (d) ₹65
39. 39.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 3 days (d) 4 days
40. 40.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹26 (d) ₹78

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