Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 461 · 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.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹45 (c) ₹63 (d) ₹9
2. 2.If 5 notebooks cost ₹65, how much do 9 notebooks cost? (a) ₹585 (b) ₹130 (c) ₹69 (d) ₹117
3. 3.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹90 (d) ₹75
4. 4.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 1 day
5. 5.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days
6. 6.If 7 notebooks cost ₹28, how much do 11 notebooks cost? (a) ₹48 (b) ₹308 (c) ₹44 (d) ₹32
7. 7.If 3 kites cost ₹57, how much do 4 kites cost? (a) ₹228 (b) ₹58 (c) ₹76 (d) ₹95
8. 8.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹252 (d) ₹126
9. 9.If 4 kites cost ₹92, how much do 8 kites cost? (a) ₹207 (b) ₹96 (c) ₹184 (d) ₹736
10. 10.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 44 days (d) 45 days
11. 11.If 9 mangoes cost ₹108, how much do 10 mangoes cost? (a) ₹132 (b) ₹1080 (c) ₹120 (d) ₹109
12. 12.If 9 kites cost ₹72, how much do 3 kites cost? (a) ₹32 (b) ₹66 (c) ₹24 (d) ₹216
13. 13.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 1 day (d) 8 days
14. 14.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹29 (b) ₹58 (c) ₹87 (d) ₹116
15. 15.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹21 (b) ₹210 (c) ₹84 (d) ₹189
16. 16.If 9 pens cost ₹99, how much do 3 pens cost? (a) ₹93 (b) ₹297 (c) ₹33 (d) ₹44
17. 17.If 3 mangoes cost ₹24, how much do 9 mangoes cost? (a) ₹72 (b) ₹216 (c) ₹80 (d) ₹30
18. 18.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹336 (c) ₹240 (d) ₹48
19. 19.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 19 days (d) 25 days
20. 20.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 12 days (d) 6 days
21. 21.If 5 kites cost ₹100, how much do 10 kites cost? (a) ₹105 (b) ₹1000 (c) ₹200 (d) ₹220
22. 22.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹48 (b) ₹36 (c) ₹12 (d) ₹42
23. 23.If 8 notebooks cost ₹136, how much do 11 notebooks cost? (a) ₹204 (b) ₹187 (c) ₹1496 (d) ₹139
24. 24.If 6 kites cost ₹60, how much do 12 kites cost? (a) ₹66 (b) ₹120 (c) ₹720 (d) ₹130
25. 25.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 7 days (d) 6 days
26. 26.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 13 days
27. 27.If 7 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹36 (b) ₹252 (c) ₹30 (d) ₹40
28. 28.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹16 (b) ₹25 (c) ₹60 (d) ₹20
29. 29.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 9 days (d) 13 days
30. 30.If 6 notebooks cost ₹66, how much do 11 notebooks cost? (a) ₹726 (b) ₹132 (c) ₹71 (d) ₹121
31. 31.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 16 days (d) 10 days
32. 32.If 6 mangoes cost ₹66, how much do 10 mangoes cost? (a) ₹660 (b) ₹110 (c) ₹70 (d) ₹121
33. 33.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹125 (b) ₹175 (c) ₹150 (d) ₹25
34. 34.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 20 days (c) 13 days (d) 17 days
35. 35.If 9 mangoes cost ₹144, how much do 10 mangoes cost? (a) ₹176 (b) ₹1440 (c) ₹160 (d) ₹145
36. 36.If 8 notebooks cost ₹128, how much do 4 notebooks cost? (a) ₹124 (b) ₹64 (c) ₹80 (d) ₹512
37. 37.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 19 days
38. 38.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 21 days (d) 22 days
39. 39.4 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
40. 40.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹275 (d) ₹200

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