Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 987 · 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 4 mangoes cost ₹52, how much do 3 mangoes cost? (a) ₹52 (b) ₹156 (c) ₹51 (d) ₹39
2. 2.If 4 pens cost ₹52, how much do 12 pens cost? (a) ₹156 (b) ₹624 (c) ₹60 (d) ₹169
3. 3.₹150 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹75 (b) ₹25 (c) ₹150 (d) ₹125
4. 4.If 6 mangoes cost ₹96, how much do 5 mangoes cost? (a) ₹96 (b) ₹480 (c) ₹80 (d) ₹95
5. 5.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 2 days (d) 3 days
6. 6.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 6 days (d) 9 days
7. 7.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 7 days
8. 8.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 4 days (d) 15 days
9. 9.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 9 days (d) 12 days
10. 10.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 1 day (d) 7 days
11. 11.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹56 (d) ₹28
12. 12.If 3 pens cost ₹18, how much do 2 pens cost? (a) ₹18 (b) ₹12 (c) ₹17 (d) ₹36
13. 13.If 7 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹64 (b) ₹57 (c) ₹72 (d) ₹448
14. 14.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹108 (b) ₹24 (c) ₹96 (d) ₹120
15. 15.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 15 days (d) 16 days
16. 16.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 28 days (d) 7 days
17. 17.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 1 day
18. 18.If 2 notebooks cost ₹38, how much do 7 notebooks cost? (a) ₹266 (b) ₹43 (c) ₹152 (d) ₹133
19. 19.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹120 (b) ₹100 (c) ₹20 (d) ₹110
20. 20.If 6 mangoes cost ₹18, how much do 9 mangoes cost? (a) ₹30 (b) ₹21 (c) ₹162 (d) ₹27
21. 21.If 6 pens cost ₹102, how much do 5 pens cost? (a) ₹102 (b) ₹101 (c) ₹510 (d) ₹85
22. 22.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹112 (b) ₹91 (c) ₹14 (d) ₹70
23. 23.If 2 mangoes cost ₹42, how much do 5 mangoes cost? (a) ₹45 (b) ₹210 (c) ₹105 (d) ₹126
24. 24.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹35 (d) ₹30
25. 25.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹230 (b) ₹322 (c) ₹46 (d) ₹276
26. 26.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹96 (d) ₹60
27. 27.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹287 (d) ₹82
28. 28.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 6 days (d) 7 days
29. 29.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 3 days (d) 17 days
30. 30.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹63 (b) ₹90 (c) ₹36 (d) ₹18
31. 31.₹451 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹328 (d) ₹287
32. 32.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 5 days (d) 45 days
33. 33.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹64 (b) ₹32 (c) ₹224 (d) ₹144
34. 34.If 2 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹168 (b) ₹84 (c) ₹98 (d) ₹32
35. 35.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 13 days (d) 23 days
36. 36.If 7 notebooks cost ₹119, how much do 4 notebooks cost? (a) ₹476 (b) ₹116 (c) ₹85 (d) ₹68
37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
38. 38.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹68
39. 39.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 12 days (d) 9 days
40. 40.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 8 days (d) 10 days

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