Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 99 · 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 7 mangoes cost ₹77, how much do 4 mangoes cost? (a) ₹74 (b) ₹308 (c) ₹44 (d) ₹55
2. 2.If 4 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹11 (b) ₹12 (c) ₹9 (d) ₹36
3. 3.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 32 days (c) 14 days (d) 33 days
4. 4.If 7 kites cost ₹161, how much do 10 kites cost? (a) ₹164 (b) ₹253 (c) ₹230 (d) ₹1610
5. 5.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 3 days (d) 2 days
6. 6.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 12 days (d) 4 days
7. 7.If 7 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹80 (b) ₹252 (c) ₹36 (d) ₹48
8. 8.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹26 (b) ₹117 (c) ₹104 (d) ₹130
9. 9.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹175 (c) ₹35 (d) ₹105
10. 10.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹49 (d) ₹42
11. 11.If 4 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹108 (b) ₹432 (c) ₹120 (d) ₹53
12. 12.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹225 (b) ₹450 (c) ₹405 (d) ₹45
13. 13.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹294 (d) ₹343
14. 14.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 17 days
15. 15.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹301 (d) ₹43
16. 16.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹13 (b) ₹18 (c) ₹24 (d) ₹36
17. 17.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹69 (b) ₹85 (c) ₹68 (d) ₹17
18. 18.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹119 (c) ₹17 (d) ₹85
19. 19.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹44 (b) ₹55 (c) ₹11 (d) ₹66
20. 20.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 8 days (d) 7 days
21. 21.If 7 notebooks cost ₹119, how much do 8 notebooks cost? (a) ₹120 (b) ₹136 (c) ₹153 (d) ₹952
22. 22.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹16 (d) ₹24
23. 23.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹138 (b) ₹161 (c) ₹46 (d) ₹184
24. 24.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹132 (b) ₹45 (c) ₹88 (d) ₹66
25. 25.If 8 pens cost ₹152, how much do 6 pens cost? (a) ₹912 (b) ₹150 (c) ₹114 (d) ₹133
26. 26.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
27. 27.If 8 kites cost ₹88, how much do 11 kites cost? (a) ₹132 (b) ₹968 (c) ₹91 (d) ₹121
28. 28.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 17 days (d) 4 days
29. 29.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 8 days (d) 16 days
30. 30.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹376 (b) ₹235 (c) ₹423 (d) ₹47
31. 31.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹13 (d) ₹26
32. 32.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹45 (d) ₹41
33. 33.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 3 days (d) 4 days
34. 34.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹198 (b) ₹22 (c) ₹143 (d) ₹88
35. 35.If 6 notebooks cost ₹102, how much do 2 notebooks cost? (a) ₹51 (b) ₹98 (c) ₹204 (d) ₹34
36. 36.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
37. 37.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹86 (b) ₹43 (c) ₹129 (d) ₹87
38. 38.If 6 notebooks cost ₹60, how much do 5 notebooks cost? (a) ₹300 (b) ₹50 (c) ₹59 (d) ₹60
39. 39.If 6 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹660 (b) ₹65 (c) ₹120 (d) ₹110
40. 40.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹16 (b) ₹48 (c) ₹96 (d) ₹80

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