Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 613 · 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.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹174 (d) ₹175
2. 2.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 4 days (d) 3 days
3. 3.If 6 mangoes cost ₹138, how much do 7 mangoes cost? (a) ₹139 (b) ₹966 (c) ₹161 (d) ₹184
4. 4.₹150 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹75 (d) ₹105
5. 5.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹49 (c) ₹14 (d) ₹98
6. 6.₹210 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹84 (d) ₹105
7. 7.If 5 mangoes cost ₹100, how much do 3 mangoes cost? (a) ₹300 (b) ₹60 (c) ₹98 (d) ₹80
8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
9. 9.If 2 kites cost ₹28, how much do 9 kites cost? (a) ₹35 (b) ₹140 (c) ₹126 (d) ₹252
10. 10.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 39 days (c) 40 days (d) 9 days
11. 11.If 8 mangoes cost ₹56, how much do 4 mangoes cost? (a) ₹224 (b) ₹52 (c) ₹35 (d) ₹28
12. 12.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹80 (c) ₹100 (d) ₹20
13. 13.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 12 days (d) 7 days
14. 14.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹32 (b) ₹48 (c) ₹16 (d) ₹40
15. 15.If 6 notebooks cost ₹138, how much do 8 notebooks cost? (a) ₹207 (b) ₹140 (c) ₹1104 (d) ₹184
16. 16.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹44 (d) ₹55
17. 17.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹211 (b) ₹35 (c) ₹210 (d) ₹245
18. 18.If 7 kites cost ₹70, how much do 10 kites cost? (a) ₹73 (b) ₹700 (c) ₹100 (d) ₹110
19. 19.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 25 days (d) 7 days
20. 20.If 2 kites cost ₹48, how much do 4 kites cost? (a) ₹192 (b) ₹50 (c) ₹120 (d) ₹96
21. 21.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 4 days (d) 9 days
22. 22.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹81 (c) ₹9 (d) ₹72
23. 23.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹140 (c) ₹35 (d) ₹175
24. 24.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹22 (b) ₹77 (c) ₹110 (d) ₹44
25. 25.If 8 notebooks cost ₹160, how much do 2 notebooks cost? (a) ₹320 (b) ₹40 (c) ₹60 (d) ₹154
26. 26.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 9 days (d) 13 days
27. 27.If 2 mangoes cost ₹8, how much do 9 mangoes cost? (a) ₹15 (b) ₹72 (c) ₹40 (d) ₹36
28. 28.If 6 notebooks cost ₹84, how much do 8 notebooks cost? (a) ₹86 (b) ₹672 (c) ₹126 (d) ₹112
29. 29.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
30. 30.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 4 days (d) 2 days
31. 31.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹63 (c) ₹84 (d) ₹42
32. 32.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹287 (b) ₹369 (c) ₹205 (d) ₹41
33. 33.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹66 (b) ₹11 (c) ₹77 (d) ₹55
34. 34.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹35 (c) ₹175 (d) ₹315
35. 35.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹196 (b) ₹140 (c) ₹28 (d) ₹168
36. 36.If 8 pens cost ₹120, how much do 4 pens cost? (a) ₹75 (b) ₹116 (c) ₹480 (d) ₹60
37. 37.If 4 mangoes cost ₹64, how much do 5 mangoes cost? (a) ₹320 (b) ₹80 (c) ₹96 (d) ₹65
38. 38.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹115 (d) ₹23
39. 39.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹104 (b) ₹91 (c) ₹13 (d) ₹26
40. 40.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹168 (b) ₹63 (c) ₹21 (d) ₹189

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