Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 792 · 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.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹187 (b) ₹136 (c) ₹34 (d) ₹238
2. 2.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
3. 3.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 17 days
4. 4.If 9 mangoes cost ₹27, how much do 4 mangoes cost? (a) ₹22 (b) ₹12 (c) ₹108 (d) ₹15
5. 5.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 13 days (d) 5 days
6. 6.If 4 pens cost ₹64, how much do 5 pens cost? (a) ₹65 (b) ₹96 (c) ₹320 (d) ₹80
7. 7.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹75 (c) ₹105 (d) ₹15
8. 8.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 19 days
9. 9.If 7 kites cost ₹35, how much do 11 kites cost? (a) ₹385 (b) ₹60 (c) ₹55 (d) ₹39
10. 10.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹185 (b) ₹259 (c) ₹333 (d) ₹37
11. 11.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 13 days (d) 12 days
12. 12.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹54 (b) ₹42 (c) ₹6 (d) ₹30
13. 13.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 40 days (d) 39 days
14. 14.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 11 days (d) 28 days
15. 15.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 5 days
16. 16.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 6 days (d) 48 days
17. 17.If 9 pens cost ₹72, how much do 10 pens cost? (a) ₹720 (b) ₹73 (c) ₹88 (d) ₹80
18. 18.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 16 days (d) 7 days
19. 19.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 18 days (c) 10 days (d) 43 days
20. 20.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹156 (b) ₹78 (c) ₹117 (d) ₹39
21. 21.If 4 pens cost ₹84, how much do 2 pens cost? (a) ₹168 (b) ₹82 (c) ₹42 (d) ₹63
22. 22.If 4 mangoes cost ₹20, how much do 5 mangoes cost? (a) ₹30 (b) ₹25 (c) ₹100 (d) ₹21
23. 23.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 6 days (d) 21 days
24. 24.₹280 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹180 (c) ₹100 (d) ₹20
25. 25.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 6 days (d) 5 days
26. 26.If 6 pens cost ₹36, how much do 9 pens cost? (a) ₹39 (b) ₹324 (c) ₹54 (d) ₹60
27. 27.If 3 kites cost ₹36, how much do 12 kites cost? (a) ₹45 (b) ₹144 (c) ₹432 (d) ₹156
28. 28.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹51 (b) ₹34 (c) ₹17 (d) ₹68
29. 29.If 4 mangoes cost ₹96, how much do 3 mangoes cost? (a) ₹96 (b) ₹72 (c) ₹288 (d) ₹95
30. 30.If 8 pens cost ₹112, how much do 4 pens cost? (a) ₹448 (b) ₹56 (c) ₹108 (d) ₹70
31. 31.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 4 days
32. 32.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹315 (d) ₹280
33. 33.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹216 (b) ₹168 (c) ₹24 (d) ₹120
34. 34.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹45 (d) ₹50
35. 35.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹45 (d) ₹15
36. 36.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹37 (b) ₹259 (c) ₹222 (d) ₹185
37. 37.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹441 (b) ₹245 (c) ₹49 (d) ₹343
38. 38.If 5 notebooks cost ₹50, how much do 12 notebooks cost? (a) ₹130 (b) ₹120 (c) ₹600 (d) ₹57
39. 39.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 5 days
40. 40.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹110 (b) ₹143 (c) ₹176 (d) ₹22

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