Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 957 · 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 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹84 (b) ₹64 (c) ₹252 (d) ₹105
2. 2.If 9 kites cost ₹162, how much do 12 kites cost? (a) ₹165 (b) ₹216 (c) ₹1944 (d) ₹234
3. 3.If 4 kites cost ₹64, how much do 11 kites cost? (a) ₹192 (b) ₹704 (c) ₹176 (d) ₹71
4. 4.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹120 (b) ₹15 (c) ₹105 (d) ₹60
5. 5.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹119 (d) ₹136
6. 6.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹128 (b) ₹160 (c) ₹32 (d) ₹96
7. 7.If 6 kites cost ₹114, how much do 2 kites cost? (a) ₹57 (b) ₹38 (c) ₹110 (d) ₹228
8. 8.₹28 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹21 (d) ₹28
9. 9.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 7 days
10. 10.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 17 days (c) 9 days (d) 11 days
11. 11.If 9 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹66 (b) ₹60 (c) ₹55 (d) ₹540
12. 12.If 4 pens cost ₹32, how much do 2 pens cost? (a) ₹24 (b) ₹30 (c) ₹16 (d) ₹64
13. 13.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹238 (b) ₹170 (c) ₹34 (d) ₹306
14. 14.If 5 kites cost ₹60, how much do 11 kites cost? (a) ₹144 (b) ₹132 (c) ₹660 (d) ₹66
15. 15.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 5 days (d) 7 days
16. 16.If 6 kites cost ₹84, how much do 4 kites cost? (a) ₹70 (b) ₹336 (c) ₹82 (d) ₹56
17. 17.If 2 kites cost ₹22, how much do 8 kites cost? (a) ₹88 (b) ₹28 (c) ₹99 (d) ₹176
18. 18.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 1 day (c) 11 days (d) 21 days
19. 19.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 8 days (d) 2 days
20. 20.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 41 days (c) 20 days (d) 10 days
21. 21.If 5 mangoes cost ₹110, how much do 12 mangoes cost? (a) ₹286 (b) ₹1320 (c) ₹117 (d) ₹264
22. 22.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 2 days
23. 23.₹160 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹96 (d) ₹32
24. 24.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹23 (d) ₹46
25. 25.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 10 days
26. 26.If 7 notebooks cost ₹63, how much do 8 notebooks cost? (a) ₹64 (b) ₹504 (c) ₹81 (d) ₹72
27. 27.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹72 (b) ₹84 (c) ₹12 (d) ₹42
28. 28.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹180 (b) ₹165 (c) ₹150 (d) ₹30
29. 29.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹361 (b) ₹360 (c) ₹45 (d) ₹405
30. 30.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹47 (b) ₹376 (c) ₹94 (d) ₹329
31. 31.If 9 pens cost ₹153, how much do 5 pens cost? (a) ₹765 (b) ₹102 (c) ₹149 (d) ₹85
32. 32.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹162 (d) ₹90
33. 33.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹189 (c) ₹168 (d) ₹42
34. 34.If 5 pens cost ₹50, how much do 3 pens cost? (a) ₹150 (b) ₹40 (c) ₹48 (d) ₹30
35. 35.If 5 kites cost ₹90, how much do 11 kites cost? (a) ₹990 (b) ₹216 (c) ₹198 (d) ₹96
36. 36.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹160 (b) ₹200 (c) ₹40 (d) ₹180
37. 37.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 17 days (d) 13 days
38. 38.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹68 (d) ₹136
39. 39.If 6 mangoes cost ₹90, how much do 5 mangoes cost? (a) ₹75 (b) ₹90 (c) ₹89 (d) ₹450
40. 40.If 4 kites cost ₹88, how much do 7 kites cost? (a) ₹176 (b) ₹616 (c) ₹154 (d) ₹91

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