Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 794 · 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. 1.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 3 days
2. 2.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹28 (d) ₹21
3. 3.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 4 days (d) 16 days
4. 4.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹51 (d) ₹34
5. 5.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹369 (d) ₹410
6. 6.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹115 (d) ₹138
7. 7.If 4 mangoes cost ₹16, how much do 9 mangoes cost? (a) ₹36 (b) ₹144 (c) ₹21 (d) ₹40
8. 8.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹210 (d) ₹90
9. 9.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹41 (b) ₹83 (c) ₹82 (d) ₹123
10. 10.If 4 kites cost ₹84, how much do 7 kites cost? (a) ₹588 (b) ₹87 (c) ₹147 (d) ₹168
11. 11.If 9 kites cost ₹162, how much do 3 kites cost? (a) ₹486 (b) ₹54 (c) ₹72 (d) ₹156
12. 12.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 4 days (d) 36 days
13. 13.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹52 (b) ₹8 (c) ₹40 (d) ₹64
14. 14.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 5 days
15. 15.If 3 notebooks cost ₹57, how much do 5 notebooks cost? (a) ₹114 (b) ₹59 (c) ₹285 (d) ₹95
16. 16.If 2 mangoes cost ₹10, how much do 6 mangoes cost? (a) ₹35 (b) ₹30 (c) ₹60 (d) ₹14
17. 17.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹84 (d) ₹98
18. 18.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 11 days
19. 19.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹66 (b) ₹121 (c) ₹22 (d) ₹176
20. 20.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 10 days (d) 11 days
21. 21.If 5 mangoes cost ₹20, how much do 8 mangoes cost? (a) ₹32 (b) ₹160 (c) ₹36 (d) ₹23
22. 22.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 15 days (d) 26 days
23. 23.If 6 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹60 (b) ₹324 (c) ₹54 (d) ₹39
24. 24.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 48 days (b) 21 days (c) 3 days (d) 4 days
25. 25.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹16 (b) ₹128 (c) ₹24 (d) ₹58
26. 26.If 3 pens cost ₹12, how much do 10 pens cost? (a) ₹120 (b) ₹44 (c) ₹19 (d) ₹40
27. 27.If 9 notebooks cost ₹225, how much do 2 notebooks cost? (a) ₹50 (b) ₹450 (c) ₹75 (d) ₹218
28. 28.If 3 pens cost ₹72, how much do 8 pens cost? (a) ₹576 (b) ₹192 (c) ₹77 (d) ₹216
29. 29.₹242 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹132 (d) ₹121
30. 30.If 3 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹156 (b) ₹432 (c) ₹45 (d) ₹144
31. 31.₹442 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹221 (b) ₹306 (c) ₹136 (d) ₹34
32. 32.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹169 (b) ₹208 (c) ₹26 (d) ₹130
33. 33.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 15 days (d) 1 day
34. 34.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 5 days (d) 15 days
35. 35.If 4 pens cost ₹12, how much do 11 pens cost? (a) ₹19 (b) ₹132 (c) ₹33 (d) ₹36
36. 36.₹240 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹120 (b) ₹72 (c) ₹168 (d) ₹24
37. 37.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹30 (c) ₹60 (d) ₹165
38. 38.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹164 (b) ₹328 (c) ₹287 (d) ₹41
39. 39.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹33 (b) ₹44 (c) ₹22 (d) ₹11
40. 40.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹160 (b) ₹128 (c) ₹144 (d) ₹32

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