Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 943 · 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.₹143 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹13 (d) ₹117
2. 2.₹56 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹28 (b) ₹21 (c) ₹7 (d) ₹35
3. 3.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹60 (d) ₹120
4. 4.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹361 (d) ₹360
5. 5.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹15 (c) ₹10 (d) ₹5
6. 6.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹140 (b) ₹110 (c) ₹20 (d) ₹80
7. 7.If 2 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹63 (b) ₹126 (c) ₹72 (d) ₹23
8. 8.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 2 days (d) 3 days
9. 9.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 2 days
10. 10.If 5 kites cost ₹115, how much do 11 kites cost? (a) ₹253 (b) ₹276 (c) ₹121 (d) ₹1265
11. 11.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 27 days (d) 15 days
12. 12.If 3 mangoes cost ₹18, how much do 2 mangoes cost? (a) ₹12 (b) ₹36 (c) ₹18 (d) ₹17
13. 13.If 7 mangoes cost ₹161, how much do 4 mangoes cost? (a) ₹158 (b) ₹644 (c) ₹115 (d) ₹92
14. 14.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 6 days (d) 13 days
15. 15.₹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
16. 16.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹108 (b) ₹48 (c) ₹24 (d) ₹168
17. 17.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹198 (d) ₹99
18. 18.If 9 mangoes cost ₹126, how much do 6 mangoes cost? (a) ₹756 (b) ₹84 (c) ₹123 (d) ₹98
19. 19.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹387 (d) ₹430
20. 20.₹310 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹310 (d) ₹279
21. 21.If 2 pens cost ₹16, how much do 3 pens cost? (a) ₹32 (b) ₹24 (c) ₹17 (d) ₹48
22. 22.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹45 (b) ₹60 (c) ₹30 (d) ₹15
23. 23.If 4 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹45 (b) ₹220 (c) ₹66 (d) ₹55
24. 24.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 1 day (d) 7 days
25. 25.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹70 (d) ₹98
26. 26.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹266 (b) ₹209 (c) ₹38 (d) ₹152
27. 27.If 6 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹37 (b) ₹252 (c) ₹48 (d) ₹42
28. 28.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
29. 29.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 30 days (c) 13 days (d) 31 days
30. 30.If 9 notebooks cost ₹216, how much do 10 notebooks cost? (a) ₹264 (b) ₹217 (c) ₹2160 (d) ₹240
31. 31.If 6 kites cost ₹114, how much do 5 kites cost? (a) ₹113 (b) ₹570 (c) ₹114 (d) ₹95
32. 32.If 2 mangoes cost ₹16, how much do 9 mangoes cost? (a) ₹72 (b) ₹80 (c) ₹144 (d) ₹23
33. 33.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 4 days (d) 25 days
34. 34.If 8 mangoes cost ₹200, how much do 7 mangoes cost? (a) ₹200 (b) ₹175 (c) ₹199 (d) ₹1400
35. 35.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 1 day (d) 8 days
36. 36.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹441 (b) ₹343 (c) ₹245 (d) ₹49
37. 37.₹222 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹185 (b) ₹111 (c) ₹37 (d) ₹222
38. 38.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹294 (c) ₹42 (d) ₹210
39. 39.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
40. 40.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 12 days (d) 2 days

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