Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 801 · 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.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹128 (b) ₹64 (c) ₹96 (d) ₹32
2. 2.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹84 (b) ₹85 (c) ₹105 (d) ₹21
3. 3.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹88 (d) ₹110
4. 4.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹56 (b) ₹42 (c) ₹70 (d) ₹14
5. 5.4 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) 6 days (d) 5 days
6. 6.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹60 (b) ₹84 (c) ₹72 (d) ₹12
7. 7.If 4 pens cost ₹72, how much do 2 pens cost? (a) ₹144 (b) ₹54 (c) ₹70 (d) ₹36
8. 8.₹238 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹204 (b) ₹119 (c) ₹238 (d) ₹34
9. 9.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 9 days (d) 14 days
10. 10.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹13 (b) ₹130 (c) ₹65 (d) ₹117
11. 11.If 5 mangoes cost ₹45, how much do 2 mangoes cost? (a) ₹27 (b) ₹90 (c) ₹18 (d) ₹42
12. 12.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹102 (d) ₹17
13. 13.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹35 (d) ₹49
14. 14.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 10 days (d) 3 days
15. 15.If 7 kites cost ₹21, how much do 8 kites cost? (a) ₹22 (b) ₹24 (c) ₹27 (d) ₹168
16. 16.If 8 kites cost ₹128, how much do 9 kites cost? (a) ₹129 (b) ₹160 (c) ₹1152 (d) ₹144
17. 17.If 8 notebooks cost ₹56, how much do 10 notebooks cost? (a) ₹77 (b) ₹70 (c) ₹58 (d) ₹560
18. 18.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 6 days (d) 5 days
19. 19.If 4 pens cost ₹100, how much do 10 pens cost? (a) ₹106 (b) ₹1000 (c) ₹275 (d) ₹250
20. 20.If 4 pens cost ₹32, how much do 2 pens cost? (a) ₹30 (b) ₹24 (c) ₹64 (d) ₹16
21. 21.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹256 (b) ₹208 (c) ₹32 (d) ₹160
22. 22.If 4 kites cost ₹40, how much do 11 kites cost? (a) ₹47 (b) ₹440 (c) ₹110 (d) ₹120
23. 23.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 1 day (d) 7 days
24. 24.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹20 (b) ₹48 (c) ₹16 (d) ₹13
25. 25.If 9 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹33 (b) ₹270 (c) ₹28 (d) ₹30
26. 26.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 3 days (d) 29 days
27. 27.If 3 pens cost ₹57, how much do 2 pens cost? (a) ₹114 (b) ₹57 (c) ₹38 (d) ₹56
28. 28.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹175 (b) ₹151 (c) ₹150 (d) ₹25
29. 29.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 48 days (c) 3 days (d) 18 days
30. 30.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹91 (d) ₹117
31. 31.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 6 days (d) 12 days
32. 32.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹46 (b) ₹23 (c) ₹115 (d) ₹138
33. 33.If 9 mangoes cost ₹54, how much do 6 mangoes cost? (a) ₹36 (b) ₹42 (c) ₹51 (d) ₹324
34. 34.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹160 (b) ₹144 (c) ₹32 (d) ₹128
35. 35.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 11 days (d) 16 days
36. 36.If 6 kites cost ₹108, how much do 9 kites cost? (a) ₹111 (b) ₹180 (c) ₹972 (d) ₹162
37. 37.If 3 pens cost ₹33, how much do 7 pens cost? (a) ₹37 (b) ₹77 (c) ₹88 (d) ₹231
38. 38.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹55 (c) ₹40 (d) ₹70
39. 39.If 3 pens cost ₹24, how much do 11 pens cost? (a) ₹32 (b) ₹96 (c) ₹88 (d) ₹264
40. 40.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 16 days (d) 4 days

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