Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 208 · 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 5 pens cost ₹35, how much do 2 pens cost? (a) ₹70 (b) ₹14 (c) ₹21 (d) ₹32
2. 2.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹30 (b) ₹180 (c) ₹150 (d) ₹90
3. 3.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 4 days
4. 4.If 2 kites cost ₹40, how much do 4 kites cost? (a) ₹80 (b) ₹100 (c) ₹160 (d) ₹42
5. 5.₹168 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹28 (b) ₹168 (c) ₹84 (d) ₹140
6. 6.₹405 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹270 (d) ₹225
7. 7.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹33 (b) ₹297 (c) ₹264 (d) ₹165
8. 8.If 2 notebooks cost ₹42, how much do 3 notebooks cost? (a) ₹63 (b) ₹126 (c) ₹84 (d) ₹43
9. 9.If 6 pens cost ₹96, how much do 9 pens cost? (a) ₹160 (b) ₹99 (c) ₹144 (d) ₹864
10. 10.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 1 day (d) 13 days
11. 11.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹222 (d) ₹37
12. 12.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
13. 13.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹75 (b) ₹25 (c) ₹100 (d) ₹125
14. 14.If 6 mangoes cost ₹102, how much do 10 mangoes cost? (a) ₹187 (b) ₹170 (c) ₹106 (d) ₹1020
15. 15.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹205 (b) ₹165 (c) ₹164 (d) ₹41
16. 16.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 11 days (c) 10 days (d) 12 days
17. 17.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹28 (b) ₹126 (c) ₹196 (d) ₹56
18. 18.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 16 days (d) 6 days
19. 19.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 11 days (d) 5 days
20. 20.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹81 (b) ₹9 (c) ₹63 (d) ₹45
21. 21.If 6 kites cost ₹60, how much do 4 kites cost? (a) ₹40 (b) ₹58 (c) ₹50 (d) ₹240
22. 22.If 8 pens cost ₹168, how much do 2 pens cost? (a) ₹42 (b) ₹336 (c) ₹63 (d) ₹162
23. 23.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹312 (d) ₹273
24. 24.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹60 (c) ₹12 (d) ₹48
25. 25.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹52 (b) ₹78 (c) ₹13 (d) ₹65
26. 26.If 5 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹44 (b) ₹72 (c) ₹80 (d) ₹360
27. 27.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹50 (b) ₹45 (c) ₹10 (d) ₹5
28. 28.If 5 kites cost ₹105, how much do 4 kites cost? (a) ₹104 (b) ₹84 (c) ₹105 (d) ₹420
29. 29.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹232 (b) ₹116 (c) ₹203 (d) ₹29
30. 30.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹98 (d) ₹77
31. 31.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 1 day (d) 10 days
32. 32.If 9 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹63 (b) ₹56 (c) ₹62 (d) ₹504
33. 33.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 13 days (d) 6 days
34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
35. 35.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹7 (b) ₹43 (c) ₹42 (d) ₹49
36. 36.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 45 days (d) 21 days
37. 37.If 6 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹77 (b) ₹462 (c) ₹84 (d) ₹47
38. 38.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 8 days (d) 7 days
39. 39.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 43 days (c) 7 days (d) 17 days
40. 40.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 2 days (d) 12 days

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