Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 168 · 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.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹196 (c) ₹28 (d) ₹252
2. 2.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 18 days
3. 3.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹103 (b) ₹102 (c) ₹119 (d) ₹17
4. 4.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹72 (b) ₹96 (c) ₹120 (d) ₹24
5. 5.If 7 kites cost ₹112, how much do 3 kites cost? (a) ₹336 (b) ₹64 (c) ₹48 (d) ₹108
6. 6.If 2 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹240 (b) ₹49 (c) ₹440 (d) ₹220
7. 7.If 9 pens cost ₹153, how much do 2 pens cost? (a) ₹146 (b) ₹34 (c) ₹51 (d) ₹306
8. 8.If 5 mangoes cost ₹35, how much do 11 mangoes cost? (a) ₹84 (b) ₹385 (c) ₹77 (d) ₹41
9. 9.If 8 pens cost ₹32, how much do 3 pens cost? (a) ₹96 (b) ₹27 (c) ₹16 (d) ₹12
10. 10.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹248 (b) ₹31 (c) ₹249 (d) ₹279
11. 11.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹125 (b) ₹100 (c) ₹76 (d) ₹300
12. 12.If 9 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹47 (b) ₹12 (c) ₹108 (d) ₹18
13. 13.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹87 (b) ₹145 (c) ₹116 (d) ₹29
14. 14.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 20 days (d) 21 days
15. 15.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 14 days (d) 24 days
16. 16.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹81 (b) ₹135 (c) ₹189 (d) ₹27
17. 17.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 21 days (d) 20 days
18. 18.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 9 days (d) 8 days
19. 19.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 1 day
20. 20.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹88 (b) ₹16 (c) ₹80 (d) ₹96
21. 21.If 8 kites cost ₹144, how much do 10 kites cost? (a) ₹180 (b) ₹198 (c) ₹146 (d) ₹1440
22. 22.If 6 pens cost ₹90, how much do 2 pens cost? (a) ₹45 (b) ₹30 (c) ₹86 (d) ₹180
23. 23.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹35 (d) ₹30
24. 24.If 2 pens cost ₹24, how much do 3 pens cost? (a) ₹25 (b) ₹72 (c) ₹48 (d) ₹36
25. 25.If 2 pens cost ₹38, how much do 6 pens cost? (a) ₹228 (b) ₹114 (c) ₹133 (d) ₹42
26. 26.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹287 (b) ₹205 (c) ₹246 (d) ₹41
27. 27.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 9 days (d) 10 days
28. 28.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
29. 29.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 9 days
30. 30.If 3 pens cost ₹51, how much do 10 pens cost? (a) ₹170 (b) ₹187 (c) ₹510 (d) ₹58
31. 31.If 6 kites cost ₹60, how much do 8 kites cost? (a) ₹62 (b) ₹480 (c) ₹80 (d) ₹90
32. 32.If 4 notebooks cost ₹52, how much do 11 notebooks cost? (a) ₹143 (b) ₹572 (c) ₹59 (d) ₹156
33. 33.If 4 pens cost ₹16, how much do 2 pens cost? (a) ₹12 (b) ₹32 (c) ₹8 (d) ₹14
34. 34.₹245 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹49 (b) ₹197 (c) ₹245 (d) ₹196
35. 35.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 1 day (d) 7 days
36. 36.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹153 (c) ₹136 (d) ₹17
37. 37.If 3 mangoes cost ₹39, how much do 11 mangoes cost? (a) ₹156 (b) ₹143 (c) ₹429 (d) ₹47
38. 38.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 8 days (d) 6 days
39. 39.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹45 (d) ₹15
40. 40.If 5 kites cost ₹25, how much do 4 kites cost? (a) ₹24 (b) ₹100 (c) ₹25 (d) ₹20

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