Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 88 · 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.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹65 (b) ₹91 (c) ₹78 (d) ₹13
2. 2.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹17 (b) ₹24 (c) ₹20 (d) ₹80
3. 3.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹1584 (b) ₹177 (c) ₹220 (d) ₹198
4. 4.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 8 days (d) 9 days
5. 5.If 3 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹96 (b) ₹25 (c) ₹32 (d) ₹40
6. 6.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹52 (d) ₹234
7. 7.If 7 mangoes cost ₹98, how much do 4 mangoes cost? (a) ₹392 (b) ₹56 (c) ₹95 (d) ₹70
8. 8.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹32 (c) ₹256 (d) ₹160
9. 9.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 20 days (c) 5 days (d) 21 days
10. 10.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 24 days (b) 7 days (c) 18 days (d) 6 days
11. 11.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 6 days (d) 7 days
12. 12.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹50 (d) ₹60
13. 13.If 2 kites cost ₹6, how much do 12 kites cost? (a) ₹36 (b) ₹16 (c) ₹39 (d) ₹72
14. 14.If 7 notebooks cost ₹84, how much do 12 notebooks cost? (a) ₹156 (b) ₹89 (c) ₹1008 (d) ₹144
15. 15.If 6 notebooks cost ₹18, how much do 3 notebooks cost? (a) ₹54 (b) ₹9 (c) ₹12 (d) ₹15
16. 16.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 9 days (d) 11 days
17. 17.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹283 (d) ₹282
18. 18.₹42 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹6 (b) ₹21 (c) ₹36 (d) ₹42
19. 19.If 2 notebooks cost ₹10, how much do 4 notebooks cost? (a) ₹40 (b) ₹12 (c) ₹25 (d) ₹20
20. 20.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹48 (d) ₹96
21. 21.If 8 pens cost ₹152, how much do 11 pens cost? (a) ₹228 (b) ₹1672 (c) ₹209 (d) ₹155
22. 22.If 5 mangoes cost ₹35, how much do 9 mangoes cost? (a) ₹63 (b) ₹39 (c) ₹70 (d) ₹315
23. 23.If 3 pens cost ₹66, how much do 2 pens cost? (a) ₹44 (b) ₹132 (c) ₹66 (d) ₹65
24. 24.If 2 pens cost ₹18, how much do 9 pens cost? (a) ₹162 (b) ₹25 (c) ₹81 (d) ₹90
25. 25.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹169 (d) ₹208
26. 26.If 2 kites cost ₹34, how much do 5 kites cost? (a) ₹102 (b) ₹170 (c) ₹85 (d) ₹37
27. 27.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹104 (d) ₹52
28. 28.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 4 days (d) 12 days
29. 29.If 7 pens cost ₹161, how much do 6 pens cost? (a) ₹160 (b) ₹138 (c) ₹966 (d) ₹161
30. 30.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 6 days
31. 31.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹70 (b) ₹28 (c) ₹14 (d) ₹49
32. 32.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹14 (d) ₹70
33. 33.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹189 (b) ₹42 (c) ₹210 (d) ₹168
34. 34.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹98 (b) ₹70 (c) ₹84 (d) ₹14
35. 35.If 9 notebooks cost ₹144, how much do 10 notebooks cost? (a) ₹1440 (b) ₹160 (c) ₹176 (d) ₹145
36. 36.If 3 kites cost ₹72, how much do 12 kites cost? (a) ₹288 (b) ₹312 (c) ₹81 (d) ₹864
37. 37.If 3 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹19 (b) ₹30 (c) ₹24 (d) ₹72
38. 38.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 7 days (c) 19 days (d) 52 days
39. 39.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 22 days (d) 23 days
40. 40.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 4 days (d) 25 days

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