Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 373 · 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. 1.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 13 days (d) 11 days
2. 2.If 9 notebooks cost ₹162, how much do 10 notebooks cost? (a) ₹1620 (b) ₹180 (c) ₹198 (d) ₹163
3. 3.If 4 notebooks cost ₹16, how much do 11 notebooks cost? (a) ₹176 (b) ₹48 (c) ₹44 (d) ₹23
4. 4.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 11 days (d) 10 days
5. 5.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 5 days (d) 6 days
6. 6.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹352 (b) ₹220 (c) ₹44 (d) ₹286
7. 7.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹283 (d) ₹282
8. 8.If 9 mangoes cost ₹27, how much do 12 mangoes cost? (a) ₹30 (b) ₹324 (c) ₹39 (d) ₹36
9. 9.If 3 kites cost ₹72, how much do 5 kites cost? (a) ₹144 (b) ₹74 (c) ₹120 (d) ₹360
10. 10.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
11. 11.If 3 kites cost ₹27, how much do 2 kites cost? (a) ₹27 (b) ₹26 (c) ₹18 (d) ₹54
12. 12.₹275 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹25 (b) ₹175 (c) ₹200 (d) ₹100
13. 13.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 4 days
14. 14.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 64 days (d) 63 days
15. 15.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹36 (c) ₹72 (d) ₹108
16. 16.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 6 days (d) 24 days
17. 17.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 18 days (d) 10 days
18. 18.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹35 (d) ₹140
19. 19.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹300 (b) ₹270 (c) ₹150 (d) ₹30
20. 20.If 8 notebooks cost ₹64, how much do 4 notebooks cost? (a) ₹32 (b) ₹60 (c) ₹256 (d) ₹40
21. 21.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹216 (b) ₹36 (c) ₹180 (d) ₹198
22. 22.₹250 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹225 (b) ₹250 (c) ₹25 (d) ₹125
23. 23.If 7 mangoes cost ₹147, how much do 5 mangoes cost? (a) ₹145 (b) ₹105 (c) ₹735 (d) ₹126
24. 24.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 36 days (d) 35 days
25. 25.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹336 (b) ₹288 (c) ₹240 (d) ₹48
26. 26.If 9 notebooks cost ₹99, how much do 6 notebooks cost? (a) ₹77 (b) ₹96 (c) ₹594 (d) ₹66
27. 27.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹20 (b) ₹48 (c) ₹16 (d) ₹13
28. 28.If 5 mangoes cost ₹20, how much do 12 mangoes cost? (a) ₹27 (b) ₹48 (c) ₹240 (d) ₹52
29. 29.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 1 day (d) 21 days
30. 30.If 5 kites cost ₹110, how much do 4 kites cost? (a) ₹440 (b) ₹110 (c) ₹88 (d) ₹109
31. 31.₹72 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹54 (d) ₹18
32. 32.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹105 (d) ₹140
33. 33.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹450 (d) ₹405
34. 34.₹63 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹18 (b) ₹45 (c) ₹54 (d) ₹9
35. 35.If 9 kites cost ₹72, how much do 12 kites cost? (a) ₹75 (b) ₹104 (c) ₹96 (d) ₹864
36. 36.If 5 notebooks cost ₹45, how much do 7 notebooks cost? (a) ₹47 (b) ₹315 (c) ₹72 (d) ₹63
37. 37.If 7 mangoes cost ₹28, how much do 6 mangoes cost? (a) ₹28 (b) ₹24 (c) ₹168 (d) ₹27
38. 38.If 4 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹84 (b) ₹280 (c) ₹57 (d) ₹70
39. 39.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 11 days (d) 21 days
40. 40.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹210 (b) ₹21 (c) ₹84 (d) ₹189

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