Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 844 · 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 3 notebooks cost ₹69, how much do 10 notebooks cost? (a) ₹253 (b) ₹230 (c) ₹690 (d) ₹76
2. 2.If 9 notebooks cost ₹54, how much do 7 notebooks cost? (a) ₹378 (b) ₹52 (c) ₹48 (d) ₹42
3. 3.If 5 kites cost ₹25, how much do 11 kites cost? (a) ₹31 (b) ₹55 (c) ₹275 (d) ₹60
4. 4.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 17 days (d) 13 days
5. 5.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 2 days
6. 6.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 14 days (c) 9 days (d) 8 days
7. 7.If 6 notebooks cost ₹42, how much do 9 notebooks cost? (a) ₹63 (b) ₹70 (c) ₹378 (d) ₹45
8. 8.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹121 (b) ₹110 (c) ₹132 (d) ₹22
9. 9.If 6 pens cost ₹54, how much do 12 pens cost? (a) ₹60 (b) ₹117 (c) ₹648 (d) ₹108
10. 10.If 9 kites cost ₹81, how much do 3 kites cost? (a) ₹75 (b) ₹243 (c) ₹36 (d) ₹27
11. 11.If 6 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹40 (b) ₹30 (c) ₹180 (d) ₹57
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 28 days
13. 13.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
14. 14.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 7 days (d) 6 days
15. 15.If 7 pens cost ₹154, how much do 3 pens cost? (a) ₹150 (b) ₹462 (c) ₹66 (d) ₹88
16. 16.₹517 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹141 (b) ₹376 (c) ₹47 (d) ₹423
17. 17.If 6 mangoes cost ₹96, how much do 9 mangoes cost? (a) ₹864 (b) ₹160 (c) ₹144 (d) ₹99
18. 18.If 8 pens cost ₹72, how much do 7 pens cost? (a) ₹72 (b) ₹63 (c) ₹504 (d) ₹71
19. 19.If 3 kites cost ₹24, how much do 7 kites cost? (a) ₹168 (b) ₹56 (c) ₹28 (d) ₹64
20. 20.If 7 mangoes cost ₹168, how much do 10 mangoes cost? (a) ₹1680 (b) ₹171 (c) ₹240 (d) ₹264
21. 21.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹196 (b) ₹98 (c) ₹49 (d) ₹147
22. 22.If 8 pens cost ₹104, how much do 4 pens cost? (a) ₹65 (b) ₹100 (c) ₹52 (d) ₹416
23. 23.If 3 kites cost ₹48, how much do 4 kites cost? (a) ₹49 (b) ₹192 (c) ₹80 (d) ₹64
24. 24.If 2 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹72 (b) ₹48 (c) ₹25 (d) ₹36
25. 25.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹387 (b) ₹301 (c) ₹215 (d) ₹43
26. 26.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹104 (d) ₹117
27. 27.If 9 pens cost ₹144, how much do 12 pens cost? (a) ₹147 (b) ₹208 (c) ₹192 (d) ₹1728
28. 28.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹180 (d) ₹108
29. 29.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹306 (b) ₹119 (c) ₹102 (d) ₹54
30. 30.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹54 (b) ₹63 (c) ₹9 (d) ₹45
31. 31.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 4 days (d) 9 days
32. 32.If 7 notebooks cost ₹119, how much do 8 notebooks cost? (a) ₹136 (b) ₹153 (c) ₹952 (d) ₹120
33. 33.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 13 days (d) 8 days
34. 34.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹84 (c) ₹112 (d) ₹98
35. 35.6 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) 5 days (d) 6 days
36. 36.If 4 notebooks cost ₹32, how much do 2 notebooks cost? (a) ₹24 (b) ₹16 (c) ₹30 (d) ₹64
37. 37.₹90 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹90 (b) ₹72 (c) ₹45 (d) ₹18
38. 38.If 5 mangoes cost ₹85, how much do 7 mangoes cost? (a) ₹87 (b) ₹595 (c) ₹136 (d) ₹119
39. 39.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹136 (b) ₹68 (c) ₹119 (d) ₹17
40. 40.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 6 days (d) 7 days

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