Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 325 · 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 2 pens cost ₹46, how much do 9 pens cost? (a) ₹207 (b) ₹230 (c) ₹414 (d) ₹53
2. 2.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹32 (b) ₹224 (c) ₹176 (d) ₹128
3. 3.If 2 pens cost ₹26, how much do 10 pens cost? (a) ₹260 (b) ₹34 (c) ₹143 (d) ₹130
4. 4.If 3 kites cost ₹12, how much do 5 kites cost? (a) ₹24 (b) ₹14 (c) ₹60 (d) ₹20
5. 5.If 6 notebooks cost ₹150, how much do 9 notebooks cost? (a) ₹225 (b) ₹1350 (c) ₹250 (d) ₹153
6. 6.₹132 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹99 (d) ₹66
7. 7.If 2 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹120 (b) ₹192 (c) ₹96 (d) ₹50
8. 8.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹328 (b) ₹205 (c) ₹369 (d) ₹41
9. 9.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹39 (b) ₹78 (c) ₹351 (d) ₹390
10. 10.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 14 days
11. 11.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 20 days (d) 6 days
12. 12.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 17 days (d) 34 days
13. 13.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹25 (c) ₹15 (d) ₹5
14. 14.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹72 (c) ₹96 (d) ₹24
15. 15.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
16. 16.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 9 days (d) 15 days
17. 17.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 52 days (d) 53 days
18. 18.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹10 (c) ₹50 (d) ₹40
19. 19.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 6 days (d) 8 days
20. 20.If 8 kites cost ₹72, how much do 10 kites cost? (a) ₹90 (b) ₹720 (c) ₹74 (d) ₹99
21. 21.If 4 notebooks cost ₹12, how much do 6 notebooks cost? (a) ₹21 (b) ₹14 (c) ₹18 (d) ₹72
22. 22.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹192 (b) ₹216 (c) ₹240 (d) ₹48
23. 23.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹220 (b) ₹320 (c) ₹40 (d) ₹120
24. 24.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
25. 25.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹225 (b) ₹200 (c) ₹50 (d) ₹250
26. 26.If 9 kites cost ₹189, how much do 4 kites cost? (a) ₹184 (b) ₹105 (c) ₹84 (d) ₹756
27. 27.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹30 (c) ₹10 (d) ₹50
28. 28.If 5 notebooks cost ₹95, how much do 12 notebooks cost? (a) ₹102 (b) ₹228 (c) ₹247 (d) ₹1140
29. 29.If 4 mangoes cost ₹28, how much do 2 mangoes cost? (a) ₹26 (b) ₹14 (c) ₹56 (d) ₹21
30. 30.If 7 notebooks cost ₹63, how much do 8 notebooks cost? (a) ₹81 (b) ₹504 (c) ₹64 (d) ₹72
31. 31.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹36 (c) ₹40 (d) ₹8
32. 32.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹12 (b) ₹66 (c) ₹84 (d) ₹48
33. 33.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹147 (b) ₹105 (c) ₹21 (d) ₹189
34. 34.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 25 days (d) 23 days
35. 35.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
36. 36.If 5 pens cost ₹30, how much do 7 pens cost? (a) ₹210 (b) ₹32 (c) ₹48 (d) ₹42
37. 37.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 11 days
38. 38.If 9 mangoes cost ₹90, how much do 4 mangoes cost? (a) ₹360 (b) ₹50 (c) ₹85 (d) ₹40
39. 39.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 14 days (d) 8 days
40. 40.If 2 kites cost ₹46, how much do 7 kites cost? (a) ₹51 (b) ₹184 (c) ₹161 (d) ₹322

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