Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 372 · 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 7 pens cost ₹168, how much do 9 pens cost? (a) ₹216 (b) ₹170 (c) ₹1512 (d) ₹240
2. 2.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹150 (c) ₹120 (d) ₹30
3. 3.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹128 (b) ₹16 (c) ₹80 (d) ₹104
4. 4.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹387 (b) ₹430 (c) ₹215 (d) ₹43
5. 5.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹25 (c) ₹50 (d) ₹10
6. 6.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹116 (b) ₹29 (c) ₹145 (d) ₹87
7. 7.If 2 pens cost ₹18, how much do 9 pens cost? (a) ₹162 (b) ₹81 (c) ₹90 (d) ₹25
8. 8.If 5 pens cost ₹60, how much do 6 pens cost? (a) ₹84 (b) ₹61 (c) ₹360 (d) ₹72
9. 9.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹12 (b) ₹108 (c) ₹22 (d) ₹15
10. 10.If 3 mangoes cost ₹12, how much do 2 mangoes cost? (a) ₹11 (b) ₹8 (c) ₹24 (d) ₹12
11. 11.If 6 kites cost ₹126, how much do 3 kites cost? (a) ₹378 (b) ₹84 (c) ₹123 (d) ₹63
12. 12.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹68 (b) ₹51 (c) ₹17 (d) ₹34
13. 13.If 2 notebooks cost ₹46, how much do 9 notebooks cost? (a) ₹414 (b) ₹53 (c) ₹230 (d) ₹207
14. 14.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 18 days (d) 19 days
15. 15.If 9 pens cost ₹36, how much do 8 pens cost? (a) ₹32 (b) ₹36 (c) ₹288 (d) ₹35
16. 16.If 9 pens cost ₹135, how much do 2 pens cost? (a) ₹270 (b) ₹128 (c) ₹45 (d) ₹30
17. 17.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 3 days (d) 16 days
18. 18.If 4 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹15 (b) ₹20 (c) ₹60 (d) ₹19
19. 19.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹17 (d) ₹68
20. 20.If 5 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹28 (b) ₹32 (c) ₹22 (d) ₹140
21. 21.If 5 notebooks cost ₹40, how much do 4 notebooks cost? (a) ₹39 (b) ₹40 (c) ₹160 (d) ₹32
22. 22.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹225 (d) ₹315
23. 23.If 5 pens cost ₹50, how much do 6 pens cost? (a) ₹70 (b) ₹60 (c) ₹51 (d) ₹300
24. 24.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹8 (d) ₹32
25. 25.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹147 (c) ₹21 (d) ₹126
26. 26.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹72 (b) ₹144 (c) ₹18 (d) ₹126
27. 27.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 15 days (c) 5 days (d) 36 days
28. 28.If 3 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹126 (b) ₹42 (c) ₹48 (d) ₹22
29. 29.If 8 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹81 (b) ₹100 (c) ₹720 (d) ₹90
30. 30.₹384 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹48 (b) ₹336 (c) ₹192 (d) ₹384
31. 31.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 8 days
32. 32.₹480 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹480 (b) ₹432 (c) ₹240 (d) ₹48
33. 33.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹37 (b) ₹333 (c) ₹111 (d) ₹296
34. 34.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 7 days
35. 35.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 12 days (d) 13 days
36. 36.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 1 day (d) 13 days
37. 37.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 25 days (d) 9 days
38. 38.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹30 (b) ₹90 (c) ₹180 (d) ₹150
39. 39.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 9 days (d) 14 days
40. 40.If 7 kites cost ₹154, how much do 10 kites cost? (a) ₹157 (b) ₹1540 (c) ₹242 (d) ₹220

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