Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 714 · 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 mangoes cost ₹96, how much do 11 mangoes cost? (a) ₹1056 (b) ₹99 (c) ₹132 (d) ₹144
2. 2.If 7 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹58 (b) ₹27 (c) ₹126 (d) ₹18
3. 3.₹480 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹240 (b) ₹480 (c) ₹432 (d) ₹48
4. 4.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 37 days (d) 36 days
5. 5.If 4 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹19 (b) ₹20 (c) ₹15 (d) ₹60
6. 6.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹147 (d) ₹189
7. 7.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹27 (b) ₹217 (c) ₹243 (d) ₹216
8. 8.If 3 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹110 (b) ₹88 (c) ₹67 (d) ₹264
9. 9.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 45 days (d) 5 days
10. 10.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹198 (b) ₹72 (c) ₹36 (d) ₹324
11. 11.If 2 kites cost ₹48, how much do 12 kites cost? (a) ₹288 (b) ₹312 (c) ₹58 (d) ₹576
12. 12.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 32 days (c) 2 days (d) 14 days
13. 13.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 11 days (d) 1 day
14. 14.If 6 pens cost ₹114, how much do 7 pens cost? (a) ₹152 (b) ₹798 (c) ₹115 (d) ₹133
15. 15.If 4 notebooks cost ₹60, how much do 11 notebooks cost? (a) ₹165 (b) ₹67 (c) ₹660 (d) ₹180
16. 16.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹71 (b) ₹35 (c) ₹70 (d) ₹105
17. 17.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹160 (b) ₹20 (c) ₹60 (d) ₹110
18. 18.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹75 (b) ₹60 (c) ₹90 (d) ₹30
19. 19.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 3 days (d) 21 days
20. 20.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹390 (c) ₹351 (d) ₹39
21. 21.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 2 days
22. 22.If 2 notebooks cost ₹20, how much do 5 notebooks cost? (a) ₹60 (b) ₹100 (c) ₹23 (d) ₹50
23. 23.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹114 (b) ₹19 (c) ₹76 (d) ₹95
24. 24.If 2 notebooks cost ₹14, how much do 5 notebooks cost? (a) ₹35 (b) ₹42 (c) ₹17 (d) ₹70
25. 25.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹19 (b) ₹133 (c) ₹171 (d) ₹95
26. 26.If 5 pens cost ₹75, how much do 2 pens cost? (a) ₹150 (b) ₹72 (c) ₹45 (d) ₹30
27. 27.If 5 kites cost ₹105, how much do 2 kites cost? (a) ₹63 (b) ₹210 (c) ₹42 (d) ₹102
28. 28.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 14 days (d) 10 days
29. 29.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹185 (d) ₹333
30. 30.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 17 days
31. 31.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹108 (b) ₹22 (c) ₹15 (d) ₹12
32. 32.If 2 mangoes cost ₹50, how much do 10 mangoes cost? (a) ₹58 (b) ₹275 (c) ₹500 (d) ₹250
33. 33.₹100 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹40 (d) ₹50
34. 34.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹50 (c) ₹25 (d) ₹45
35. 35.If 4 kites cost ₹16, how much do 6 kites cost? (a) ₹18 (b) ₹96 (c) ₹24 (d) ₹28
36. 36.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 7 days (d) 2 days
37. 37.If 2 pens cost ₹44, how much do 10 pens cost? (a) ₹440 (b) ₹242 (c) ₹220 (d) ₹52
38. 38.If 3 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹576 (b) ₹208 (c) ₹57 (d) ₹192
39. 39.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 19 days (d) 12 days
40. 40.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹114 (b) ₹76 (c) ₹38 (d) ₹57

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