Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 908 · 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.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹66 (d) ₹77
2. 2.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹34 (b) ₹132 (c) ₹44 (d) ₹55
3. 3.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹123 (c) ₹164 (d) ₹205
4. 4.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹200 (b) ₹175 (c) ₹100 (d) ₹25
5. 5.If 8 notebooks cost ₹144, how much do 9 notebooks cost? (a) ₹180 (b) ₹145 (c) ₹1296 (d) ₹162
6. 6.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 16 days (d) 11 days
7. 7.If 9 mangoes cost ₹162, how much do 7 mangoes cost? (a) ₹144 (b) ₹1134 (c) ₹160 (d) ₹126
8. 8.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹72 (b) ₹48 (c) ₹60 (d) ₹24
9. 9.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 3 days
10. 10.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 6 days (c) 18 days (d) 12 days
11. 11.If 6 mangoes cost ₹90, how much do 7 mangoes cost? (a) ₹630 (b) ₹105 (c) ₹91 (d) ₹120
12. 12.If 2 notebooks cost ₹32, how much do 10 notebooks cost? (a) ₹160 (b) ₹40 (c) ₹176 (d) ₹320
13. 13.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 6 days
14. 14.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 7 days (c) 32 days (d) 17 days
15. 15.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 35 days (c) 11 days (d) 36 days
16. 16.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 10 days
17. 17.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹21 (c) ₹105 (d) ₹126
18. 18.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 15 days (c) 7 days (d) 22 days
19. 19.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹56 (b) ₹29 (c) ₹42 (d) ₹84
20. 20.If 6 kites cost ₹120, how much do 10 kites cost? (a) ₹1200 (b) ₹124 (c) ₹220 (d) ₹200
21. 21.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹66 (b) ₹24 (c) ₹108 (d) ₹12
22. 22.₹480 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹48 (b) ₹480 (c) ₹432 (d) ₹240
23. 23.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹306 (b) ₹238 (c) ₹34 (d) ₹170
24. 24.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹86 (d) ₹215
25. 25.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 3 days (d) 18 days
26. 26.If 3 mangoes cost ₹9, how much do 9 mangoes cost? (a) ₹30 (b) ₹15 (c) ₹81 (d) ₹27
27. 27.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 17 days (d) 9 days
28. 28.If 9 mangoes cost ₹225, how much do 11 mangoes cost? (a) ₹2475 (b) ₹227 (c) ₹275 (d) ₹300
29. 29.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 21 days (d) 22 days
30. 30.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹125 (b) ₹100 (c) ₹25 (d) ₹150
31. 31.If 6 mangoes cost ₹150, how much do 10 mangoes cost? (a) ₹275 (b) ₹250 (c) ₹154 (d) ₹1500
32. 32.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹190 (d) ₹228
33. 33.If 8 notebooks cost ₹24, how much do 11 notebooks cost? (a) ₹27 (b) ₹33 (c) ₹36 (d) ₹264
34. 34.If 8 pens cost ₹184, how much do 12 pens cost? (a) ₹276 (b) ₹299 (c) ₹2208 (d) ₹188
35. 35.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 21 days (d) 22 days
36. 36.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 17 days (d) 13 days
37. 37.If 4 notebooks cost ₹28, how much do 2 notebooks cost? (a) ₹21 (b) ₹14 (c) ₹56 (d) ₹26
38. 38.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 11 days
39. 39.If 6 pens cost ₹30, how much do 9 pens cost? (a) ₹270 (b) ₹33 (c) ₹45 (d) ₹50
40. 40.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days

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