Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 150 · 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. 1.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 20 days (d) 14 days
2. 2.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹192 (b) ₹160 (c) ₹96 (d) ₹32
3. 3.If 7 notebooks cost ₹91, how much do 11 notebooks cost? (a) ₹1001 (b) ₹95 (c) ₹156 (d) ₹143
4. 4.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹160 (d) ₹96
5. 5.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹169 (b) ₹26 (c) ₹234 (d) ₹104
6. 6.If 2 mangoes cost ₹6, how much do 4 mangoes cost? (a) ₹8 (b) ₹15 (c) ₹12 (d) ₹24
7. 7.If 9 mangoes cost ₹189, how much do 8 mangoes cost? (a) ₹168 (b) ₹188 (c) ₹1512 (d) ₹189
8. 8.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹39 (b) ₹234 (c) ₹195 (d) ₹156
9. 9.If 3 kites cost ₹36, how much do 4 kites cost? (a) ₹144 (b) ₹60 (c) ₹37 (d) ₹48
10. 10.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 31 days (d) 30 days
11. 11.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹102 (b) ₹119 (c) ₹85 (d) ₹17
12. 12.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 4 days (d) 19 days
13. 13.If 2 pens cost ₹26, how much do 11 pens cost? (a) ₹143 (b) ₹35 (c) ₹286 (d) ₹156
14. 14.₹154 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹77 (b) ₹42 (c) ₹14 (d) ₹112
15. 15.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹160 (c) ₹120 (d) ₹40
16. 16.If 3 pens cost ₹63, how much do 9 pens cost? (a) ₹210 (b) ₹69 (c) ₹567 (d) ₹189
17. 17.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 6 days (d) 7 days
18. 18.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
19. 19.If 6 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹840 (b) ₹140 (c) ₹160 (d) ₹121
20. 20.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹312 (b) ₹351 (c) ₹39 (d) ₹195
21. 21.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹9 (d) ₹54
22. 22.If 8 pens cost ₹160, how much do 12 pens cost? (a) ₹260 (b) ₹1920 (c) ₹240 (d) ₹164
23. 23.If 8 mangoes cost ₹64, how much do 3 mangoes cost? (a) ₹24 (b) ₹32 (c) ₹59 (d) ₹192
24. 24.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 2 days (c) 3 days (d) 4 days
25. 25.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 16 days (d) 12 days
26. 26.₹144 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹72 (b) ₹48 (c) ₹144 (d) ₹96
27. 27.If 9 mangoes cost ₹225, how much do 10 mangoes cost? (a) ₹226 (b) ₹250 (c) ₹275 (d) ₹2250
28. 28.If 2 kites cost ₹34, how much do 7 kites cost? (a) ₹238 (b) ₹136 (c) ₹119 (d) ₹39
29. 29.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹50 (d) ₹20
30. 30.If 9 mangoes cost ₹171, how much do 2 mangoes cost? (a) ₹164 (b) ₹342 (c) ₹38 (d) ₹57
31. 31.If 3 kites cost ₹75, how much do 4 kites cost? (a) ₹125 (b) ₹76 (c) ₹300 (d) ₹100
32. 32.If 2 pens cost ₹46, how much do 9 pens cost? (a) ₹207 (b) ₹230 (c) ₹414 (d) ₹53
33. 33.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹141 (b) ₹140 (c) ₹35 (d) ₹175
34. 34.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
35. 35.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹50 (d) ₹25
36. 36.If 2 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹80 (b) ₹60 (c) ₹41 (d) ₹120
37. 37.If 9 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹108 (b) ₹47 (c) ₹12 (d) ₹18
38. 38.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹21 (b) ₹189 (c) ₹168 (d) ₹105
39. 39.If 9 mangoes cost ₹216, how much do 3 mangoes cost? (a) ₹96 (b) ₹72 (c) ₹210 (d) ₹648
40. 40.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 27 days (d) 3 days

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