Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 427 · 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 7 notebooks cost ₹49, how much do 9 notebooks cost? (a) ₹63 (b) ₹51 (c) ₹441 (d) ₹70
2. 2.If 7 kites cost ₹147, how much do 9 kites cost? (a) ₹149 (b) ₹1323 (c) ₹189 (d) ₹210
3. 3.If 4 pens cost ₹88, how much do 11 pens cost? (a) ₹264 (b) ₹242 (c) ₹968 (d) ₹95
4. 4.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹280 (b) ₹35 (c) ₹245 (d) ₹140
5. 5.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 36 days (d) 37 days
6. 6.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹110 (d) ₹180
7. 7.If 2 kites cost ₹16, how much do 6 kites cost? (a) ₹20 (b) ₹96 (c) ₹56 (d) ₹48
8. 8.If 9 pens cost ₹153, how much do 8 pens cost? (a) ₹136 (b) ₹152 (c) ₹153 (d) ₹1224
9. 9.If 7 kites cost ₹98, how much do 9 kites cost? (a) ₹882 (b) ₹126 (c) ₹140 (d) ₹100
10. 10.If 6 mangoes cost ₹102, how much do 2 mangoes cost? (a) ₹51 (b) ₹204 (c) ₹98 (d) ₹34
11. 11.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
12. 12.If 4 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹84 (b) ₹21 (c) ₹28 (d) ₹27
13. 13.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹70 (b) ₹56 (c) ₹14 (d) ₹35
14. 14.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹60 (b) ₹70 (c) ₹80 (d) ₹20
15. 15.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹275 (d) ₹250
16. 16.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹180 (b) ₹210 (c) ₹105 (d) ₹30
17. 17.If 8 pens cost ₹32, how much do 7 pens cost? (a) ₹31 (b) ₹28 (c) ₹32 (d) ₹224
18. 18.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 17 days
19. 19.If 7 pens cost ₹119, how much do 5 pens cost? (a) ₹117 (b) ₹102 (c) ₹85 (d) ₹595
20. 20.If 2 mangoes cost ₹36, how much do 11 mangoes cost? (a) ₹198 (b) ₹45 (c) ₹216 (d) ₹396
21. 21.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹34 (b) ₹102 (c) ₹204 (d) ₹170
22. 22.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 6 days (d) 5 days
23. 23.If 8 kites cost ₹160, how much do 3 kites cost? (a) ₹80 (b) ₹155 (c) ₹480 (d) ₹60
24. 24.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 15 days (d) 22 days
25. 25.If 8 kites cost ₹144, how much do 6 kites cost? (a) ₹142 (b) ₹126 (c) ₹864 (d) ₹108
26. 26.If 5 mangoes cost ₹85, how much do 6 mangoes cost? (a) ₹102 (b) ₹119 (c) ₹510 (d) ₹86
27. 27.If 6 kites cost ₹30, how much do 2 kites cost? (a) ₹26 (b) ₹10 (c) ₹15 (d) ₹60
28. 28.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 3 days
29. 29.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹47 (d) ₹46
30. 30.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹52 (b) ₹39 (c) ₹65 (d) ₹13
31. 31.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹42 (b) ₹84 (c) ₹378 (d) ₹231
32. 32.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
33. 33.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹215 (d) ₹301
34. 34.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 25 days (d) 13 days
35. 35.₹75 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹75 (c) ₹50 (d) ₹25
36. 36.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹28 (d) ₹29
37. 37.If 2 kites cost ₹38, how much do 8 kites cost? (a) ₹152 (b) ₹171 (c) ₹304 (d) ₹44
38. 38.If 5 mangoes cost ₹85, how much do 9 mangoes cost? (a) ₹153 (b) ₹89 (c) ₹765 (d) ₹170
39. 39.If 3 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹33 (b) ₹96 (c) ₹104 (d) ₹288
40. 40.If 8 pens cost ₹112, how much do 5 pens cost? (a) ₹84 (b) ₹70 (c) ₹109 (d) ₹560

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