Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 420 · 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 5 kites cost ₹90, how much do 10 kites cost? (a) ₹180 (b) ₹900 (c) ₹198 (d) ₹95
2. 2.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹222 (d) ₹223
3. 3.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹26 (c) ₹78 (d) ₹52
4. 4.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 12 days (d) 2 days
5. 5.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 9 days
6. 6.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹264 (b) ₹288 (c) ₹48 (d) ₹240
7. 7.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹60 (d) ₹108
8. 8.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
9. 9.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹32 (b) ₹192 (c) ₹96 (d) ₹160
10. 10.If 3 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹37 (b) ₹144 (c) ₹48 (d) ₹60
11. 11.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 19 days (d) 3 days
12. 12.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 7 days
13. 13.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹144 (b) ₹24 (c) ₹132 (d) ₹120
14. 14.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
15. 15.If 7 mangoes cost ₹28, how much do 12 mangoes cost? (a) ₹48 (b) ₹33 (c) ₹336 (d) ₹52
16. 16.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹81 (c) ₹18 (d) ₹162
17. 17.If 8 pens cost ₹176, how much do 6 pens cost? (a) ₹1056 (b) ₹132 (c) ₹174 (d) ₹154
18. 18.If 4 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹90 (b) ₹61 (c) ₹75 (d) ₹300
19. 19.If 3 mangoes cost ₹39, how much do 8 mangoes cost? (a) ₹312 (b) ₹44 (c) ₹104 (d) ₹117
20. 20.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹225 (c) ₹25 (d) ₹250
21. 21.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
22. 22.If 6 kites cost ₹24, how much do 7 kites cost? (a) ₹25 (b) ₹32 (c) ₹168 (d) ₹28
23. 23.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹92 (c) ₹69 (d) ₹23
24. 24.₹294 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹126 (b) ₹147 (c) ₹168 (d) ₹42
25. 25.If 3 kites cost ₹54, how much do 6 kites cost? (a) ₹57 (b) ₹324 (c) ₹108 (d) ₹126
26. 26.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 19 days (d) 40 days
27. 27.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 45 days (d) 21 days
28. 28.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹100 (c) ₹250 (d) ₹50
29. 29.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹192 (b) ₹432 (c) ₹312 (d) ₹48
30. 30.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹230 (b) ₹23 (c) ₹207 (d) ₹115
31. 31.₹155 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹124 (b) ₹125 (c) ₹155 (d) ₹31
32. 32.3 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) 13 days (d) 9 days
33. 33.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹54 (c) ₹90 (d) ₹18
34. 34.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹12 (d) ₹8
35. 35.If 3 kites cost ₹27, how much do 4 kites cost? (a) ₹108 (b) ₹45 (c) ₹36 (d) ₹28
36. 36.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 12 days (d) 4 days
37. 37.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 1 day (c) 6 days (d) 7 days
38. 38.If 6 kites cost ₹54, how much do 12 kites cost? (a) ₹108 (b) ₹60 (c) ₹648 (d) ₹117
39. 39.₹207 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹207 (d) ₹185
40. 40.If 5 kites cost ₹55, how much do 3 kites cost? (a) ₹53 (b) ₹44 (c) ₹33 (d) ₹165

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