Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 680 · 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 4 kites cost ₹72, how much do 5 kites cost? (a) ₹90 (b) ₹108 (c) ₹73 (d) ₹360
2. 2.If 7 pens cost ₹21, how much do 9 pens cost? (a) ₹23 (b) ₹27 (c) ₹30 (d) ₹189
3. 3.If 8 pens cost ₹152, how much do 9 pens cost? (a) ₹1368 (b) ₹190 (c) ₹153 (d) ₹171
4. 4.₹72 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹36 (b) ₹63 (c) ₹9 (d) ₹72
5. 5.If 5 pens cost ₹100, how much do 10 pens cost? (a) ₹105 (b) ₹220 (c) ₹1000 (d) ₹200
6. 6.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹140 (b) ₹350 (c) ₹35 (d) ₹315
7. 7.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 4 days
8. 8.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹1584 (b) ₹198 (c) ₹220 (d) ₹177
9. 9.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 4 days (d) 9 days
10. 10.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹22 (b) ₹33 (c) ₹44 (d) ₹11
11. 11.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
12. 12.If 3 mangoes cost ₹21, how much do 5 mangoes cost? (a) ₹42 (b) ₹23 (c) ₹105 (d) ₹35
13. 13.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹21 (b) ₹28 (c) ₹7 (d) ₹14
14. 14.If 3 mangoes cost ₹27, how much do 8 mangoes cost? (a) ₹32 (b) ₹72 (c) ₹81 (d) ₹216
15. 15.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹30 (d) ₹25
16. 16.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹46 (b) ₹253 (c) ₹230 (d) ₹276
17. 17.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 12 days (d) 6 days
18. 18.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 10 days (c) 2 days (d) 14 days
19. 19.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹68 (d) ₹85
20. 20.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹94 (b) ₹376 (c) ₹47 (d) ₹329
21. 21.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹78 (d) ₹65
22. 22.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 6 days (d) 7 days
23. 23.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 6 days (d) 4 days
24. 24.₹210 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹168 (b) ₹105 (c) ₹42 (d) ₹210
25. 25.If 6 kites cost ₹24, how much do 7 kites cost? (a) ₹25 (b) ₹32 (c) ₹28 (d) ₹168
26. 26.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 15 days (d) 16 days
27. 27.₹240 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹144 (d) ₹120
28. 28.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 10 days (d) 16 days
29. 29.If 3 mangoes cost ₹12, how much do 11 mangoes cost? (a) ₹48 (b) ₹44 (c) ₹20 (d) ₹132
30. 30.If 3 notebooks cost ₹48, how much do 8 notebooks cost? (a) ₹53 (b) ₹384 (c) ₹128 (d) ₹144
31. 31.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹49 (b) ₹147 (c) ₹245 (d) ₹343
32. 32.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹184 (b) ₹92 (c) ₹161 (d) ₹23
33. 33.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 32 days (c) 33 days (d) 17 days
34. 34.₹315 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹281 (b) ₹315 (c) ₹280 (d) ₹35
35. 35.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹80 (b) ₹120 (c) ₹40 (d) ₹100
36. 36.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 11 days (d) 7 days
37. 37.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 11 days (d) 25 days
38. 38.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹232 (d) ₹203
39. 39.If 5 notebooks cost ₹60, how much do 2 notebooks cost? (a) ₹120 (b) ₹24 (c) ₹57 (d) ₹36
40. 40.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹24 (d) ₹16

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