Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 501 · 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 8 pens cost ₹48, how much do 2 pens cost? (a) ₹12 (b) ₹42 (c) ₹96 (d) ₹18
2. 2.If 8 kites cost ₹152, how much do 9 kites cost? (a) ₹1368 (b) ₹153 (c) ₹190 (d) ₹171
3. 3.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹11 (b) ₹110 (c) ₹44 (d) ₹99
4. 4.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹48 (c) ₹96 (d) ₹24
5. 5.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹138 (d) ₹161
6. 6.If 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹35 (b) ₹140 (c) ₹28 (d) ₹34
7. 7.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹60 (c) ₹55 (d) ₹10
8. 8.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 28 days (d) 3 days
9. 9.₹143 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹13 (b) ₹26 (c) ₹130 (d) ₹117
10. 10.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 33 days (d) 5 days
11. 11.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹82 (b) ₹287 (c) ₹41 (d) ₹328
12. 12.₹189 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹84 (d) ₹126
13. 13.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹234 (d) ₹169
14. 14.If 5 pens cost ₹95, how much do 3 pens cost? (a) ₹93 (b) ₹57 (c) ₹76 (d) ₹285
15. 15.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 11 days
16. 16.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 6 days (d) 5 days
17. 17.If 9 mangoes cost ₹189, how much do 2 mangoes cost? (a) ₹182 (b) ₹63 (c) ₹378 (d) ₹42
18. 18.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹240 (b) ₹144 (c) ₹48 (d) ₹288
19. 19.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 41 days (c) 16 days (d) 40 days
20. 20.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹5 (b) ₹10 (c) ₹20 (d) ₹15
21. 21.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
22. 22.If 4 pens cost ₹56, how much do 12 pens cost? (a) ₹182 (b) ₹64 (c) ₹672 (d) ₹168
23. 23.If 6 kites cost ₹24, how much do 11 kites cost? (a) ₹44 (b) ₹48 (c) ₹29 (d) ₹264
24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 17 days (d) 13 days
25. 25.If 2 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹192 (b) ₹53 (c) ₹336 (d) ₹168
26. 26.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 12 days
27. 27.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 13 days
28. 28.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹70 (b) ₹140 (c) ₹105 (d) ₹35
29. 29.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 5 days (d) 14 days
30. 30.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 4 days (d) 8 days
31. 31.If 7 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹28 (b) ₹168 (c) ₹24 (d) ₹27
32. 32.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 8 days (d) 18 days
33. 33.If 6 pens cost ₹96, how much do 8 pens cost? (a) ₹98 (b) ₹128 (c) ₹144 (d) ₹768
34. 34.If 3 notebooks cost ₹54, how much do 9 notebooks cost? (a) ₹162 (b) ₹60 (c) ₹180 (d) ₹486
35. 35.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹49 (c) ₹70 (d) ₹14
36. 36.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 19 days (d) 2 days
37. 37.If 8 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹840 (b) ₹120 (c) ₹119 (d) ₹105
38. 38.If 6 notebooks cost ₹114, how much do 5 notebooks cost? (a) ₹114 (b) ₹570 (c) ₹113 (d) ₹95
39. 39.If 3 pens cost ₹63, how much do 12 pens cost? (a) ₹273 (b) ₹756 (c) ₹72 (d) ₹252
40. 40.If 5 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹90 (b) ₹18 (c) ₹24 (d) ₹28

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