Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 819 · 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. 1.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 3 days (d) 2 days
2. 2.If 7 mangoes cost ₹35, how much do 8 mangoes cost? (a) ₹40 (b) ₹45 (c) ₹280 (d) ₹36
3. 3.If 7 kites cost ₹126, how much do 11 kites cost? (a) ₹198 (b) ₹1386 (c) ₹216 (d) ₹130
4. 4.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹108 (b) ₹288 (c) ₹36 (d) ₹198
5. 5.If 4 kites cost ₹20, how much do 12 kites cost? (a) ₹240 (b) ₹28 (c) ₹65 (d) ₹60
6. 6.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹243 (b) ₹189 (c) ₹27 (d) ₹135
7. 7.If 9 pens cost ₹135, how much do 6 pens cost? (a) ₹105 (b) ₹132 (c) ₹810 (d) ₹90
8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 26 days (d) 27 days
9. 9.If 8 kites cost ₹80, how much do 9 kites cost? (a) ₹81 (b) ₹720 (c) ₹90 (d) ₹100
10. 10.₹170 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹136 (b) ₹85 (c) ₹34 (d) ₹170
11. 11.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹203 (d) ₹174
12. 12.If 6 mangoes cost ₹96, how much do 8 mangoes cost? (a) ₹98 (b) ₹144 (c) ₹128 (d) ₹768
13. 13.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 14 days (d) 15 days
14. 14.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹55 (b) ₹33 (c) ₹11 (d) ₹44
15. 15.If 7 mangoes cost ₹49, how much do 11 mangoes cost? (a) ₹539 (b) ₹53 (c) ₹84 (d) ₹77
16. 16.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 3 days (c) 15 days (d) 37 days
17. 17.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹18 (d) ₹48
18. 18.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 26 days (c) 27 days (d) 28 days
19. 19.If 2 mangoes cost ₹32, how much do 8 mangoes cost? (a) ₹256 (b) ₹144 (c) ₹38 (d) ₹128
20. 20.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 8 days (d) 13 days
21. 21.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹10 (b) ₹100 (c) ₹50 (d) ₹90
22. 22.If 8 kites cost ₹56, how much do 3 kites cost? (a) ₹51 (b) ₹21 (c) ₹168 (d) ₹28
23. 23.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹153 (b) ₹136 (c) ₹17 (d) ₹137
24. 24.If 6 pens cost ₹66, how much do 11 pens cost? (a) ₹726 (b) ₹121 (c) ₹71 (d) ₹132
25. 25.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
26. 26.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹225 (d) ₹250
27. 27.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹42 (b) ₹378 (c) ₹294 (d) ₹210
28. 28.If 3 kites cost ₹24, how much do 11 kites cost? (a) ₹32 (b) ₹96 (c) ₹264 (d) ₹88
29. 29.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹40 (d) ₹8
30. 30.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹264 (b) ₹132 (c) ₹231 (d) ₹33
31. 31.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 6 days (d) 8 days
32. 32.If 6 kites cost ₹96, how much do 2 kites cost? (a) ₹48 (b) ₹192 (c) ₹92 (d) ₹32
33. 33.If 2 pens cost ₹50, how much do 10 pens cost? (a) ₹275 (b) ₹500 (c) ₹58 (d) ₹250
34. 34.If 8 pens cost ₹40, how much do 11 pens cost? (a) ₹440 (b) ₹43 (c) ₹55 (d) ₹60
35. 35.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹37 (b) ₹296 (c) ₹333 (d) ₹297
36. 36.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 27 days (d) 15 days
37. 37.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹108 (b) ₹12 (c) ₹54 (d) ₹96
38. 38.₹376 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹376 (b) ₹188 (c) ₹47 (d) ₹329
39. 39.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 20 days
40. 40.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹54 (b) ₹27 (c) ₹108 (d) ₹81

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