Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 352 · 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. 1.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
2. 2.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹155 (b) ₹217 (c) ₹186 (d) ₹31
3. 3.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹5 (b) ₹41 (c) ₹40 (d) ₹45
4. 4.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹105 (b) ₹13 (c) ₹104 (d) ₹117
5. 5.If 3 kites cost ₹39, how much do 8 kites cost? (a) ₹312 (b) ₹104 (c) ₹44 (d) ₹117
6. 6.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 22 days (d) 1 day
7. 7.If 5 notebooks cost ₹85, how much do 10 notebooks cost? (a) ₹90 (b) ₹187 (c) ₹850 (d) ₹170
8. 8.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 15 days
9. 9.If 4 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹21 (b) ₹15 (c) ₹24 (d) ₹84
10. 10.If 2 notebooks cost ₹26, how much do 7 notebooks cost? (a) ₹104 (b) ₹182 (c) ₹91 (d) ₹31
11. 11.If 9 notebooks cost ₹171, how much do 4 notebooks cost? (a) ₹684 (b) ₹95 (c) ₹166 (d) ₹76
12. 12.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹270 (d) ₹210
13. 13.If 4 pens cost ₹56, how much do 2 pens cost? (a) ₹42 (b) ₹112 (c) ₹54 (d) ₹28
14. 14.If 4 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹28 (b) ₹54 (c) ₹42 (d) ₹112
15. 15.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹12 (d) ₹18
16. 16.If 3 kites cost ₹30, how much do 8 kites cost? (a) ₹35 (b) ₹240 (c) ₹90 (d) ₹80
17. 17.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 17 days (d) 5 days
18. 18.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹50 (c) ₹10 (d) ₹45
19. 19.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹99 (b) ₹72 (c) ₹126 (d) ₹18
20. 20.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 7 days
21. 21.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 37 days (c) 15 days (d) 1 day
22. 22.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 7 days
23. 23.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹114 (d) ₹95
24. 24.If 3 kites cost ₹24, how much do 2 kites cost? (a) ₹16 (b) ₹23 (c) ₹48 (d) ₹24
25. 25.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹154 (d) ₹66
26. 26.If 3 notebooks cost ₹75, how much do 2 notebooks cost? (a) ₹75 (b) ₹74 (c) ₹150 (d) ₹50
27. 27.If 2 notebooks cost ₹34, how much do 10 notebooks cost? (a) ₹170 (b) ₹42 (c) ₹340 (d) ₹187
28. 28.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹112 (c) ₹63 (d) ₹14
29. 29.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 19 days (b) 16 days (c) 12 days (d) 18 days
30. 30.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 13 days (d) 16 days
31. 31.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹57 (c) ₹39 (d) ₹38
32. 32.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹6 (b) ₹27 (c) ₹48 (d) ₹54
33. 33.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹77 (b) ₹154 (c) ₹22 (d) ₹132
34. 34.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹45 (c) ₹9 (d) ₹27
35. 35.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹252 (c) ₹42 (d) ₹294
36. 36.If 4 notebooks cost ₹100, how much do 5 notebooks cost? (a) ₹150 (b) ₹125 (c) ₹500 (d) ₹101
37. 37.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹20 (d) ₹15
38. 38.If 9 notebooks cost ₹189, how much do 3 notebooks cost? (a) ₹567 (b) ₹183 (c) ₹63 (d) ₹84
39. 39.If 4 kites cost ₹16, how much do 12 kites cost? (a) ₹48 (b) ₹52 (c) ₹192 (d) ₹24
40. 40.If 6 kites cost ₹84, how much do 7 kites cost? (a) ₹588 (b) ₹98 (c) ₹112 (d) ₹85

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