Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 45 · 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. 1.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 31 days (c) 16 days (d) 30 days
2. 2.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 17 days (d) 18 days
3. 3.If 7 mangoes cost ₹168, how much do 4 mangoes cost? (a) ₹165 (b) ₹120 (c) ₹672 (d) ₹96
4. 4.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹315 (b) ₹175 (c) ₹350 (d) ₹35
5. 5.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 10 days (d) 9 days
6. 6.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 11 days (c) 7 days (d) 8 days
7. 7.If 8 pens cost ₹200, how much do 3 pens cost? (a) ₹600 (b) ₹75 (c) ₹100 (d) ₹195
8. 8.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹78 (b) ₹52 (c) ₹65 (d) ₹13
9. 9.If 7 kites cost ₹175, how much do 5 kites cost? (a) ₹125 (b) ₹173 (c) ₹150 (d) ₹875
10. 10.If 8 mangoes cost ₹160, how much do 3 mangoes cost? (a) ₹155 (b) ₹80 (c) ₹60 (d) ₹480
11. 11.If 6 mangoes cost ₹30, how much do 9 mangoes cost? (a) ₹33 (b) ₹270 (c) ₹45 (d) ₹50
12. 12.If 7 pens cost ₹84, how much do 10 pens cost? (a) ₹840 (b) ₹87 (c) ₹132 (d) ₹120
13. 13.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
14. 14.If 4 pens cost ₹88, how much do 11 pens cost? (a) ₹95 (b) ₹264 (c) ₹968 (d) ₹242
15. 15.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 11 days (d) 2 days
16. 16.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹259 (b) ₹222 (c) ₹37 (d) ₹223
17. 17.If 9 notebooks cost ₹99, how much do 3 notebooks cost? (a) ₹297 (b) ₹93 (c) ₹44 (d) ₹33
18. 18.If 7 mangoes cost ₹154, how much do 2 mangoes cost? (a) ₹44 (b) ₹149 (c) ₹308 (d) ₹66
19. 19.If 3 kites cost ₹57, how much do 9 kites cost? (a) ₹513 (b) ₹63 (c) ₹190 (d) ₹171
20. 20.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹126 (c) ₹42 (d) ₹294
21. 21.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹140 (c) ₹245 (d) ₹280
22. 22.If 3 kites cost ₹18, how much do 4 kites cost? (a) ₹72 (b) ₹30 (c) ₹19 (d) ₹24
23. 23.If 5 mangoes cost ₹115, how much do 10 mangoes cost? (a) ₹230 (b) ₹1150 (c) ₹120 (d) ₹253
24. 24.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹18 (c) ₹6 (d) ₹15
25. 25.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 16 days (c) 4 days (d) 8 days
26. 26.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹13 (b) ₹15 (c) ₹60 (d) ₹18
27. 27.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
28. 28.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹30 (d) ₹60
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
30. 30.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹175 (b) ₹210 (c) ₹35 (d) ₹245
31. 31.If 3 kites cost ₹39, how much do 4 kites cost? (a) ₹65 (b) ₹40 (c) ₹156 (d) ₹52
32. 32.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 34 days (b) 5 days (c) 33 days (d) 17 days
33. 33.If 3 kites cost ₹63, how much do 8 kites cost? (a) ₹68 (b) ₹504 (c) ₹189 (d) ₹168
34. 34.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 30 days (c) 31 days (d) 12 days
35. 35.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹74 (b) ₹259 (c) ₹37 (d) ₹296
36. 36.If 4 kites cost ₹48, how much do 6 kites cost? (a) ₹72 (b) ₹288 (c) ₹50 (d) ₹84
37. 37.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 29 days (c) 13 days (d) 28 days
38. 38.If 9 pens cost ₹198, how much do 5 pens cost? (a) ₹990 (b) ₹110 (c) ₹194 (d) ₹132
39. 39.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹111 (b) ₹74 (c) ₹75 (d) ₹37
40. 40.If 5 pens cost ₹35, how much do 8 pens cost? (a) ₹56 (b) ₹63 (c) ₹280 (d) ₹38

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