Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 512 · 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 kites cost ₹27, how much do 4 kites cost? (a) ₹36 (b) ₹45 (c) ₹28 (d) ₹108
2. 2.If 6 pens cost ₹132, how much do 8 pens cost? (a) ₹176 (b) ₹198 (c) ₹1056 (d) ₹134
3. 3.If 2 kites cost ₹34, how much do 6 kites cost? (a) ₹38 (b) ₹204 (c) ₹119 (d) ₹102
4. 4.If 2 pens cost ₹10, how much do 6 pens cost? (a) ₹14 (b) ₹60 (c) ₹30 (d) ₹35
5. 5.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹34 (b) ₹204 (c) ₹238 (d) ₹170
6. 6.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹35 (c) ₹63 (d) ₹7
7. 7.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 13 days (d) 7 days
8. 8.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹91 (d) ₹104
9. 9.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 27 days (d) 3 days
10. 10.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹264 (b) ₹432 (c) ₹48 (d) ₹96
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) 27 days (c) 15 days (d) 26 days
12. 12.If 5 pens cost ₹100, how much do 6 pens cost? (a) ₹140 (b) ₹120 (c) ₹600 (d) ₹101
13. 13.If 7 mangoes cost ₹35, how much do 10 mangoes cost? (a) ₹50 (b) ₹38 (c) ₹350 (d) ₹55
14. 14.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹224 (b) ₹32 (c) ₹112 (d) ₹192
15. 15.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 4 days (d) 16 days
16. 16.If 5 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹210 (b) ₹42 (c) ₹32 (d) ₹48
17. 17.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 27 days (c) 10 days (d) 26 days
18. 18.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹35 (b) ₹140 (c) ₹105 (d) ₹70
19. 19.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹259 (b) ₹185 (c) ₹37 (d) ₹222
20. 20.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
21. 21.If 3 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹64 (b) ₹192 (c) ₹49 (d) ₹80
22. 22.If 3 pens cost ₹21, how much do 11 pens cost? (a) ₹84 (b) ₹77 (c) ₹29 (d) ₹231
23. 23.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 10 days (c) 20 days (d) 41 days
24. 24.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 7 days (d) 9 days
25. 25.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹155 (b) ₹93 (c) ₹31 (d) ₹124
26. 26.3 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) 3 days (d) 4 days
27. 27.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹252 (b) ₹28 (c) ₹58 (d) ₹35
28. 28.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 27 days (d) 13 days
29. 29.If 6 pens cost ₹54, how much do 4 pens cost? (a) ₹52 (b) ₹216 (c) ₹36 (d) ₹45
30. 30.If 6 mangoes cost ₹150, how much do 3 mangoes cost? (a) ₹75 (b) ₹450 (c) ₹147 (d) ₹100
31. 31.If 2 mangoes cost ₹26, how much do 11 mangoes cost? (a) ₹286 (b) ₹156 (c) ₹143 (d) ₹35
32. 32.If 8 notebooks cost ₹56, how much do 7 notebooks cost? (a) ₹55 (b) ₹49 (c) ₹392 (d) ₹56
33. 33.If 3 mangoes cost ₹15, how much do 5 mangoes cost? (a) ₹30 (b) ₹75 (c) ₹25 (d) ₹17
34. 34.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹32 (d) ₹44
35. 35.If 9 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹49 (b) ₹216 (c) ₹24 (d) ₹30
36. 36.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 4 days (d) 16 days
37. 37.₹350 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹175 (b) ₹300 (c) ₹50 (d) ₹350
38. 38.If 6 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹28 (b) ₹168 (c) ₹35 (d) ₹40
39. 39.If 8 mangoes cost ₹96, how much do 10 mangoes cost? (a) ₹132 (b) ₹98 (c) ₹120 (d) ₹960
40. 40.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 4 days (d) 9 days

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