Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 913 · 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 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
2. 2.If 8 pens cost ₹120, how much do 9 pens cost? (a) ₹150 (b) ₹121 (c) ₹135 (d) ₹1080
3. 3.If 7 mangoes cost ₹168, how much do 4 mangoes cost? (a) ₹120 (b) ₹672 (c) ₹96 (d) ₹165
4. 4.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 28 days (d) 11 days
5. 5.If 9 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹48 (b) ₹360 (c) ₹40 (d) ₹68
6. 6.₹147 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹127 (b) ₹126 (c) ₹21 (d) ₹147
7. 7.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 16 days (c) 31 days (d) 4 days
8. 8.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹84 (d) ₹63
9. 9.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹351 (b) ₹390 (c) ₹195 (d) ₹39
10. 10.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 20 days (d) 21 days
11. 11.If 8 pens cost ₹24, how much do 11 pens cost? (a) ₹33 (b) ₹264 (c) ₹36 (d) ₹27
12. 12.If 5 mangoes cost ₹55, how much do 2 mangoes cost? (a) ₹22 (b) ₹52 (c) ₹110 (d) ₹33
13. 13.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹283 (b) ₹329 (c) ₹282 (d) ₹47
14. 14.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 13 days (d) 14 days
15. 15.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 3 days (d) 4 days
16. 16.If 2 mangoes cost ₹6, how much do 3 mangoes cost? (a) ₹12 (b) ₹7 (c) ₹18 (d) ₹9
17. 17.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹210 (d) ₹126
18. 18.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 45 days (c) 11 days (d) 5 days
19. 19.If 8 mangoes cost ₹176, how much do 5 mangoes cost? (a) ₹173 (b) ₹880 (c) ₹110 (d) ₹132
20. 20.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹8 (b) ₹48 (c) ₹24 (d) ₹40
21. 21.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 3 days (c) 15 days (d) 37 days
22. 22.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 17 days (c) 18 days (d) 11 days
23. 23.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹6 (b) ₹42 (c) ₹54 (d) ₹30
24. 24.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 13 days (d) 7 days
25. 25.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 6 days (d) 24 days
26. 26.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹36 (d) ₹24
27. 27.If 7 notebooks cost ₹168, how much do 12 notebooks cost? (a) ₹173 (b) ₹2016 (c) ₹312 (d) ₹288
28. 28.If 2 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹108 (b) ₹37 (c) ₹54 (d) ₹72
29. 29.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹132 (b) ₹72 (c) ₹192 (d) ₹24
30. 30.If 7 pens cost ₹105, how much do 12 pens cost? (a) ₹1260 (b) ₹180 (c) ₹195 (d) ₹110
31. 31.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹40 (d) ₹24
32. 32.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 10 days (d) 8 days
33. 33.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 10 days (d) 8 days
34. 34.If 7 pens cost ₹98, how much do 2 pens cost? (a) ₹196 (b) ₹93 (c) ₹28 (d) ₹42
35. 35.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 11 days (d) 18 days
36. 36.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹144 (b) ₹54 (c) ₹18 (d) ₹99
37. 37.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 6 days
38. 38.₹117 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹90 (b) ₹9 (c) ₹36 (d) ₹81
39. 39.₹266 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹266 (b) ₹228 (c) ₹133 (d) ₹38
40. 40.If 2 kites cost ₹30, how much do 3 kites cost? (a) ₹90 (b) ₹31 (c) ₹45 (d) ₹60

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