Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 570 · 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 2 mangoes cost ₹26, how much do 5 mangoes cost? (a) ₹78 (b) ₹65 (c) ₹29 (d) ₹130
2. 2.If 8 kites cost ₹40, how much do 3 kites cost? (a) ₹120 (b) ₹35 (c) ₹15 (d) ₹20
3. 3.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 5 days (d) 21 days
4. 4.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 13 days (d) 21 days
5. 5.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹120 (b) ₹90 (c) ₹60 (d) ₹30
6. 6.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 57 days (c) 56 days (d) 20 days
7. 7.If 9 kites cost ₹63, how much do 12 kites cost? (a) ₹84 (b) ₹756 (c) ₹91 (d) ₹66
8. 8.If 5 pens cost ₹45, how much do 2 pens cost? (a) ₹90 (b) ₹27 (c) ₹18 (d) ₹42
9. 9.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹198 (b) ₹22 (c) ₹154 (d) ₹110
10. 10.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹188 (d) ₹282
11. 11.If 9 notebooks cost ₹198, how much do 2 notebooks cost? (a) ₹396 (b) ₹44 (c) ₹191 (d) ₹66
12. 12.If 3 notebooks cost ₹69, how much do 2 notebooks cost? (a) ₹46 (b) ₹69 (c) ₹68 (d) ₹138
13. 13.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 30 days (d) 31 days
14. 14.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹54 (b) ₹99 (c) ₹18 (d) ₹144
15. 15.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 3 days
16. 16.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 7 days (d) 6 days
17. 17.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 7 days (d) 15 days
18. 18.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 9 days (d) 12 days
19. 19.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹44 (d) ₹88
20. 20.If 9 notebooks cost ₹198, how much do 4 notebooks cost? (a) ₹792 (b) ₹110 (c) ₹88 (d) ₹193
21. 21.If 3 mangoes cost ₹63, how much do 9 mangoes cost? (a) ₹189 (b) ₹210 (c) ₹69 (d) ₹567
22. 22.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 20 days (d) 13 days
23. 23.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹280 (d) ₹200
24. 24.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 13 days (d) 27 days
25. 25.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹51
26. 26.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 5 days (d) 6 days
27. 27.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 13 days (d) 16 days
28. 28.If 6 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹50 (b) ₹60 (c) ₹59 (d) ₹300
29. 29.If 5 pens cost ₹105, how much do 8 pens cost? (a) ₹189 (b) ₹108 (c) ₹168 (d) ₹840
30. 30.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 10 days
31. 31.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 7 days (d) 18 days
32. 32.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 22 days (d) 21 days
33. 33.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 6 days (d) 5 days
34. 34.If 8 kites cost ₹24, how much do 4 kites cost? (a) ₹15 (b) ₹96 (c) ₹12 (d) ₹20
35. 35.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 9 days (d) 17 days
36. 36.If 8 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹70 (b) ₹480 (c) ₹78 (d) ₹60
37. 37.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹116 (d) ₹87
38. 38.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹8 (c) ₹72 (d) ₹40
39. 39.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 4 days (d) 2 days
40. 40.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 9 days (d) 15 days

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