Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 327 · 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 3 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹80 (b) ₹49 (c) ₹64 (d) ₹192
2. 2.If 2 notebooks cost ₹20, how much do 11 notebooks cost? (a) ₹220 (b) ₹120 (c) ₹29 (d) ₹110
3. 3.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 22 days (d) 21 days
4. 4.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹396 (d) ₹242
5. 5.If 6 pens cost ₹72, how much do 2 pens cost? (a) ₹68 (b) ₹36 (c) ₹144 (d) ₹24
6. 6.If 6 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹35 (b) ₹168 (c) ₹28 (d) ₹40
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) 31 days (c) 4 days (d) 16 days
8. 8.If 7 notebooks cost ₹49, how much do 9 notebooks cost? (a) ₹51 (b) ₹70 (c) ₹63 (d) ₹441
9. 9.If 2 kites cost ₹26, how much do 7 kites cost? (a) ₹31 (b) ₹104 (c) ₹182 (d) ₹91
10. 10.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 33 days (d) 34 days
11. 11.If 5 kites cost ₹110, how much do 10 kites cost? (a) ₹1100 (b) ₹242 (c) ₹115 (d) ₹220
12. 12.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 10 days (d) 11 days
13. 13.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 14 days (d) 6 days
14. 14.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹110 (b) ₹143 (c) ₹22 (d) ₹176
15. 15.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 12 days
16. 16.If 6 pens cost ₹72, how much do 7 pens cost? (a) ₹73 (b) ₹96 (c) ₹504 (d) ₹84
17. 17.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 16 days (d) 8 days
18. 18.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 5 days (d) 14 days
19. 19.₹539 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹392 (d) ₹343
20. 20.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹99 (d) ₹110
21. 21.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 9 days (d) 1 day
22. 22.If 7 kites cost ₹161, how much do 9 kites cost? (a) ₹207 (b) ₹1449 (c) ₹230 (d) ₹163
23. 23.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹47 (c) ₹69 (d) ₹23
24. 24.If 4 kites cost ₹44, how much do 5 kites cost? (a) ₹45 (b) ₹220 (c) ₹66 (d) ₹55
25. 25.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 57 days (d) 56 days
26. 26.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹33 (b) ₹99 (c) ₹165 (d) ₹198
27. 27.If 5 kites cost ₹30, how much do 8 kites cost? (a) ₹240 (b) ₹54 (c) ₹48 (d) ₹33
28. 28.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
29. 29.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
30. 30.If 9 kites cost ₹108, how much do 5 kites cost? (a) ₹104 (b) ₹540 (c) ₹60 (d) ₹72
31. 31.If 8 pens cost ₹88, how much do 3 pens cost? (a) ₹264 (b) ₹33 (c) ₹83 (d) ₹44
32. 32.If 6 pens cost ₹66, how much do 7 pens cost? (a) ₹462 (b) ₹88 (c) ₹77 (d) ₹67
33. 33.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 3 days (d) 7 days
34. 34.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹156 (b) ₹143 (c) ₹26 (d) ₹130
35. 35.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹270 (c) ₹225 (d) ₹45
36. 36.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 15 days (c) 9 days (d) 6 days
37. 37.If 2 pens cost ₹6, how much do 9 pens cost? (a) ₹13 (b) ₹27 (c) ₹54 (d) ₹30
38. 38.₹180 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹180 (c) ₹160 (d) ₹20
39. 39.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 19 days
40. 40.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 9 days (d) 16 days

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