Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 734 · 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.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹301 (d) ₹387
2. 2.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹154 (b) ₹44 (c) ₹308 (d) ₹264
3. 3.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 63 days (b) 7 days (c) 64 days (d) 21 days
4. 4.If 9 notebooks cost ₹198, how much do 10 notebooks cost? (a) ₹242 (b) ₹1980 (c) ₹220 (d) ₹199
5. 5.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 19 days (d) 11 days
6. 6.If 8 mangoes cost ₹144, how much do 5 mangoes cost? (a) ₹720 (b) ₹108 (c) ₹90 (d) ₹141
7. 7.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹62 (b) ₹31 (c) ₹124 (d) ₹93
8. 8.₹77 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹63 (c) ₹14 (d) ₹7
9. 9.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 6 days (d) 8 days
10. 10.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 20 days (d) 8 days
11. 11.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹35 (c) ₹7 (d) ₹49
12. 12.If 8 notebooks cost ₹56, how much do 5 notebooks cost? (a) ₹53 (b) ₹35 (c) ₹280 (d) ₹42
13. 13.If 9 mangoes cost ₹162, how much do 3 mangoes cost? (a) ₹72 (b) ₹54 (c) ₹486 (d) ₹156
14. 14.If 4 pens cost ₹52, how much do 11 pens cost? (a) ₹156 (b) ₹143 (c) ₹59 (d) ₹572
15. 15.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 5 days (d) 7 days
16. 16.If 2 kites cost ₹36, how much do 3 kites cost? (a) ₹37 (b) ₹108 (c) ₹54 (d) ₹72
17. 17.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹50 (c) ₹10 (d) ₹40
18. 18.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 8 days (d) 11 days
19. 19.If 9 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹54 (b) ₹48 (c) ₹432 (d) ₹53
20. 20.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
21. 21.If 9 pens cost ₹99, how much do 2 pens cost? (a) ₹92 (b) ₹22 (c) ₹33 (d) ₹198
22. 22.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 8 days (d) 20 days
23. 23.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 18 days (d) 7 days
24. 24.If 4 kites cost ₹36, how much do 11 kites cost? (a) ₹43 (b) ₹108 (c) ₹396 (d) ₹99
25. 25.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 7 days (d) 5 days
26. 26.If 7 kites cost ₹42, how much do 6 kites cost? (a) ₹42 (b) ₹41 (c) ₹36 (d) ₹252
27. 27.If 4 notebooks cost ₹96, how much do 2 notebooks cost? (a) ₹94 (b) ₹192 (c) ₹72 (d) ₹48
28. 28.If 3 kites cost ₹57, how much do 10 kites cost? (a) ₹64 (b) ₹570 (c) ₹190 (d) ₹209
29. 29.If 3 kites cost ₹9, how much do 7 kites cost? (a) ₹24 (b) ₹63 (c) ₹21 (d) ₹13
30. 30.If 7 mangoes cost ₹49, how much do 9 mangoes cost? (a) ₹51 (b) ₹63 (c) ₹70 (d) ₹441
31. 31.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹44 (b) ₹24 (c) ₹64 (d) ₹8
32. 32.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 31 days (d) 30 days
33. 33.If 5 mangoes cost ₹95, how much do 7 mangoes cost? (a) ₹97 (b) ₹133 (c) ₹152 (d) ₹665
34. 34.If 4 pens cost ₹84, how much do 6 pens cost? (a) ₹86 (b) ₹504 (c) ₹126 (d) ₹147
35. 35.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 7 days (d) 52 days
36. 36.If 5 pens cost ₹25, how much do 12 pens cost? (a) ₹60 (b) ₹65 (c) ₹300 (d) ₹32
37. 37.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 14 days (d) 9 days
38. 38.If 7 mangoes cost ₹63, how much do 11 mangoes cost? (a) ₹99 (b) ₹67 (c) ₹108 (d) ₹693
39. 39.If 3 notebooks cost ₹18, how much do 2 notebooks cost? (a) ₹36 (b) ₹17 (c) ₹18 (d) ₹12
40. 40.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹175 (d) ₹245

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