Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 112 · 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.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹33 (d) ₹44
2. 2.If 2 mangoes cost ₹10, how much do 6 mangoes cost? (a) ₹60 (b) ₹35 (c) ₹30 (d) ₹14
3. 3.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹17 (b) ₹136 (c) ₹85 (d) ₹153
4. 4.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹144 (b) ₹240 (c) ₹48 (d) ₹336
5. 5.₹351 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹312 (d) ₹313
6. 6.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹279 (b) ₹248 (c) ₹249 (d) ₹31
7. 7.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹143 (b) ₹110 (c) ₹176 (d) ₹22
8. 8.If 4 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹120 (b) ₹35 (c) ₹30 (d) ₹22
9. 9.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 18 days
10. 10.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 4 days (d) 6 days
11. 11.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
12. 12.If 3 pens cost ₹12, how much do 11 pens cost? (a) ₹48 (b) ₹20 (c) ₹44 (d) ₹132
13. 13.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 10 days (c) 27 days (d) 16 days
14. 14.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 19 days (d) 35 days
15. 15.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹16 (d) ₹64
16. 16.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 5 days (d) 13 days
17. 17.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 9 days (d) 3 days
18. 18.If 3 pens cost ₹75, how much do 7 pens cost? (a) ₹79 (b) ₹525 (c) ₹200 (d) ₹175
19. 19.If 9 kites cost ₹36, how much do 5 kites cost? (a) ₹20 (b) ₹24 (c) ₹32 (d) ₹180
20. 20.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹144 (d) ₹99
21. 21.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹273 (b) ₹195 (c) ₹234 (d) ₹39
22. 22.If 4 pens cost ₹24, how much do 7 pens cost? (a) ₹48 (b) ₹168 (c) ₹27 (d) ₹42
23. 23.If 4 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹672 (b) ₹64 (c) ₹168 (d) ₹182
24. 24.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 2 days (d) 9 days
25. 25.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹12 (b) ₹72 (c) ₹84 (d) ₹60
26. 26.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹220 (c) ₹200 (d) ₹240
27. 27.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹40 (d) ₹35
28. 28.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
29. 29.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹54 (d) ₹63
30. 30.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹8 (c) ₹64 (d) ₹36
31. 31.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 3 days
32. 32.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 17 days (d) 44 days
33. 33.If 8 kites cost ₹96, how much do 7 kites cost? (a) ₹95 (b) ₹672 (c) ₹84 (d) ₹96
34. 34.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 15 days (d) 16 days
35. 35.If 2 pens cost ₹36, how much do 4 pens cost? (a) ₹72 (b) ₹90 (c) ₹144 (d) ₹38
36. 36.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 16 days (d) 4 days
37. 37.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 23 days (d) 22 days
38. 38.If 3 kites cost ₹72, how much do 2 kites cost? (a) ₹144 (b) ₹71 (c) ₹72 (d) ₹48
39. 39.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 37 days (d) 1 day
40. 40.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹73 (b) ₹9 (c) ₹81 (d) ₹72

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