Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 364 · 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 ₹91, how much do 10 notebooks cost? (a) ₹143 (b) ₹94 (c) ₹130 (d) ₹910
2. 2.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹147 (b) ₹98 (c) ₹49 (d) ₹196
3. 3.If 5 pens cost ₹20, how much do 3 pens cost? (a) ₹18 (b) ₹60 (c) ₹16 (d) ₹12
4. 4.If 7 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹36 (b) ₹48 (c) ₹252 (d) ₹80
5. 5.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 8 days (d) 2 days
6. 6.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹15 (c) ₹60 (d) ₹45
7. 7.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹124 (b) ₹310 (c) ₹279 (d) ₹31
8. 8.If 8 kites cost ₹184, how much do 2 kites cost? (a) ₹178 (b) ₹69 (c) ₹46 (d) ₹368
9. 9.If 3 mangoes cost ₹27, how much do 4 mangoes cost? (a) ₹28 (b) ₹108 (c) ₹36 (d) ₹45
10. 10.If 9 mangoes cost ₹72, how much do 11 mangoes cost? (a) ₹792 (b) ₹88 (c) ₹74 (d) ₹96
11. 11.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 9 days (d) 8 days
12. 12.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹64 (b) ₹144 (c) ₹32 (d) ₹224
13. 13.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹149 (b) ₹185 (c) ₹37 (d) ₹148
14. 14.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 12 days
15. 15.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 19 days (d) 53 days
16. 16.If 4 kites cost ₹24, how much do 12 kites cost? (a) ₹78 (b) ₹32 (c) ₹288 (d) ₹72
17. 17.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 4 days (d) 3 days
18. 18.If 5 pens cost ₹65, how much do 8 pens cost? (a) ₹520 (b) ₹68 (c) ₹104 (d) ₹117
19. 19.If 3 mangoes cost ₹63, how much do 12 mangoes cost? (a) ₹72 (b) ₹252 (c) ₹756 (d) ₹273
20. 20.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 17 days (d) 9 days
21. 21.If 3 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹144 (b) ₹432 (c) ₹45 (d) ₹156
22. 22.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹34 (b) ₹17 (c) ₹153 (d) ₹170
23. 23.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
24. 24.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 16 days (d) 15 days
25. 25.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 13 days (d) 3 days
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) 19 days (c) 39 days (d) 40 days
27. 27.If 8 kites cost ₹192, how much do 9 kites cost? (a) ₹193 (b) ₹1728 (c) ₹240 (d) ₹216
28. 28.If 8 pens cost ₹112, how much do 10 pens cost? (a) ₹154 (b) ₹114 (c) ₹140 (d) ₹1120
29. 29.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹204 (b) ₹102 (c) ₹34 (d) ₹170
30. 30.If 6 pens cost ₹54, how much do 7 pens cost? (a) ₹55 (b) ₹72 (c) ₹63 (d) ₹378
31. 31.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹235 (b) ₹47 (c) ₹188 (d) ₹141
32. 32.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹102 (b) ₹119 (c) ₹34 (d) ₹136
33. 33.If 4 pens cost ₹44, how much do 2 pens cost? (a) ₹33 (b) ₹42 (c) ₹88 (d) ₹22
34. 34.If 3 mangoes cost ₹18, how much do 2 mangoes cost? (a) ₹36 (b) ₹18 (c) ₹12 (d) ₹17
35. 35.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹61 (b) ₹300 (c) ₹75 (d) ₹90
36. 36.If 5 mangoes cost ₹100, how much do 6 mangoes cost? (a) ₹140 (b) ₹101 (c) ₹600 (d) ₹120
37. 37.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹30 (c) ₹36 (d) ₹24
38. 38.₹441 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹294 (b) ₹196 (c) ₹49 (d) ₹245
39. 39.If 9 notebooks cost ₹135, how much do 7 notebooks cost? (a) ₹133 (b) ₹945 (c) ₹120 (d) ₹105
40. 40.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 28 days (d) 27 days

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