Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 786 · 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 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 6 days
2. 2.₹154 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹44 (b) ₹22 (c) ₹77 (d) ₹110
3. 3.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹37 (b) ₹48 (c) ₹144 (d) ₹60
4. 4.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 15 days (c) 36 days (d) 5 days
5. 5.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 10 days (d) 5 days
6. 6.If 9 kites cost ₹162, how much do 5 kites cost? (a) ₹90 (b) ₹108 (c) ₹158 (d) ₹810
7. 7.If 5 kites cost ₹90, how much do 2 kites cost? (a) ₹180 (b) ₹36 (c) ₹87 (d) ₹54
8. 8.If 2 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹48 (b) ₹72 (c) ₹36 (d) ₹25
9. 9.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹143 (c) ₹26 (d) ₹182
10. 10.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 12 days (d) 23 days
11. 11.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹242 (d) ₹264
12. 12.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 11 days (d) 10 days
13. 13.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹336 (b) ₹216 (c) ₹48 (d) ₹96
14. 14.If 2 kites cost ₹26, how much do 3 kites cost? (a) ₹52 (b) ₹78 (c) ₹39 (d) ₹27
15. 15.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹95 (b) ₹57 (c) ₹19 (d) ₹133
16. 16.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 26 days (d) 17 days
17. 17.If 5 mangoes cost ₹25, how much do 2 mangoes cost? (a) ₹10 (b) ₹50 (c) ₹22 (d) ₹15
18. 18.If 3 kites cost ₹45, how much do 4 kites cost? (a) ₹60 (b) ₹75 (c) ₹180 (d) ₹46
19. 19.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹40 (c) ₹360 (d) ₹320
20. 20.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 3 days (d) 11 days
21. 21.If 8 mangoes cost ₹128, how much do 9 mangoes cost? (a) ₹129 (b) ₹1152 (c) ₹144 (d) ₹160
22. 22.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 19 days (c) 11 days (d) 9 days
23. 23.If 6 pens cost ₹144, how much do 3 pens cost? (a) ₹96 (b) ₹72 (c) ₹432 (d) ₹141
24. 24.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 13 days (c) 30 days (d) 17 days
25. 25.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
26. 26.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 7 days (d) 8 days
27. 27.If 7 notebooks cost ₹35, how much do 12 notebooks cost? (a) ₹420 (b) ₹60 (c) ₹40 (d) ₹65
28. 28.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 1 day
29. 29.If 2 pens cost ₹24, how much do 4 pens cost? (a) ₹26 (b) ₹60 (c) ₹96 (d) ₹48
30. 30.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 39 days (c) 17 days (d) 40 days
31. 31.If 9 kites cost ₹99, how much do 4 kites cost? (a) ₹94 (b) ₹55 (c) ₹396 (d) ₹44
32. 32.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹137 (b) ₹136 (c) ₹17 (d) ₹153
33. 33.If 4 mangoes cost ₹52, how much do 5 mangoes cost? (a) ₹65 (b) ₹53 (c) ₹78 (d) ₹260
34. 34.If 2 pens cost ₹44, how much do 3 pens cost? (a) ₹88 (b) ₹66 (c) ₹132 (d) ₹45
35. 35.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 6 days (d) 5 days
36. 36.If 2 notebooks cost ₹8, how much do 6 notebooks cost? (a) ₹28 (b) ₹48 (c) ₹24 (d) ₹12
37. 37.If 8 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹53 (b) ₹35 (c) ₹280 (d) ₹42
38. 38.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 13 days
39. 39.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹70 (b) ₹49 (c) ₹28 (d) ₹14
40. 40.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹180 (b) ₹324 (c) ₹252 (d) ₹36

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