Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 769 · 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.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹70 (b) ₹50 (c) ₹90 (d) ₹10
2. 2.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 10 days
3. 3.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 17 days
4. 4.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 13 days
5. 5.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 13 days (d) 1 day
6. 6.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 8 days (d) 6 days
7. 7.If 5 kites cost ₹70, how much do 8 kites cost? (a) ₹73 (b) ₹560 (c) ₹126 (d) ₹112
8. 8.If 9 pens cost ₹126, how much do 12 pens cost? (a) ₹168 (b) ₹182 (c) ₹1512 (d) ₹129
9. 9.If 8 notebooks cost ₹136, how much do 5 notebooks cost? (a) ₹133 (b) ₹85 (c) ₹102 (d) ₹680
10. 10.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 16 days (d) 5 days
11. 11.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
12. 12.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹88 (d) ₹396
13. 13.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹80 (d) ₹72
14. 14.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 8 days (d) 2 days
15. 15.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹144 (b) ₹160 (c) ₹16 (d) ₹80
16. 16.₹343 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹294 (d) ₹98
17. 17.If 4 pens cost ₹80, how much do 10 pens cost? (a) ₹86 (b) ₹220 (c) ₹800 (d) ₹200
18. 18.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 11 days
19. 19.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹65 (b) ₹39 (c) ₹13 (d) ₹78
20. 20.If 7 kites cost ₹49, how much do 10 kites cost? (a) ₹490 (b) ₹70 (c) ₹52 (d) ₹77
21. 21.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
22. 22.If 6 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹59 (b) ₹594 (c) ₹99 (d) ₹108
23. 23.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹189 (b) ₹63 (c) ₹168 (d) ₹21
24. 24.₹429 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹39 (b) ₹351 (c) ₹117 (d) ₹312
25. 25.If 8 mangoes cost ₹24, how much do 6 mangoes cost? (a) ₹144 (b) ₹21 (c) ₹18 (d) ₹22
26. 26.If 2 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹31 (b) ₹60 (c) ₹45 (d) ₹90
27. 27.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹90 (c) ₹30 (d) ₹45
28. 28.If 4 mangoes cost ₹36, how much do 2 mangoes cost? (a) ₹18 (b) ₹72 (c) ₹34 (d) ₹27
29. 29.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 23 days (d) 7 days
30. 30.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹220 (c) ₹176 (d) ₹44
31. 31.If 9 kites cost ₹63, how much do 10 kites cost? (a) ₹630 (b) ₹70 (c) ₹64 (d) ₹77
32. 32.If 9 pens cost ₹126, how much do 5 pens cost? (a) ₹630 (b) ₹122 (c) ₹70 (d) ₹84
33. 33.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹11 (d) ₹15
34. 34.If 5 notebooks cost ₹85, how much do 4 notebooks cost? (a) ₹84 (b) ₹68 (c) ₹85 (d) ₹340
35. 35.₹196 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹168 (b) ₹28 (c) ₹196 (d) ₹98
36. 36.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹387 (d) ₹430
37. 37.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹6 (c) ₹30 (d) ₹24
38. 38.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 16 days (c) 29 days (d) 8 days
39. 39.If 6 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹48 (b) ₹252 (c) ₹42 (d) ₹37
40. 40.If 3 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹324 (b) ₹42 (c) ₹120 (d) ₹108

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