Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 588 · 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.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹117 (d) ₹156
2. 2.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹63 (d) ₹56
3. 3.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹114 (b) ₹19 (c) ₹133 (d) ₹95
4. 4.If 5 notebooks cost ₹50, how much do 12 notebooks cost? (a) ₹130 (b) ₹57 (c) ₹120 (d) ₹600
5. 5.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 10 days (d) 16 days
6. 6.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 13 days (d) 16 days
7. 7.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹105 (d) ₹120
8. 8.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 5 days (d) 12 days
9. 9.If 6 kites cost ₹66, how much do 7 kites cost? (a) ₹88 (b) ₹67 (c) ₹462 (d) ₹77
10. 10.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 6 days (d) 4 days
11. 11.If 4 pens cost ₹24, how much do 6 pens cost? (a) ₹42 (b) ₹26 (c) ₹144 (d) ₹36
12. 12.If 9 notebooks cost ₹81, how much do 10 notebooks cost? (a) ₹810 (b) ₹99 (c) ₹90 (d) ₹82
13. 13.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹24 (c) ₹16 (d) ₹8
14. 14.If 3 pens cost ₹36, how much do 12 pens cost? (a) ₹156 (b) ₹45 (c) ₹144 (d) ₹432
15. 15.If 8 notebooks cost ₹56, how much do 4 notebooks cost? (a) ₹224 (b) ₹35 (c) ₹52 (d) ₹28
16. 16.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 2 days (d) 18 days
17. 17.If 7 pens cost ₹98, how much do 12 pens cost? (a) ₹168 (b) ₹1176 (c) ₹103 (d) ₹182
18. 18.If 7 pens cost ₹42, how much do 6 pens cost? (a) ₹252 (b) ₹42 (c) ₹41 (d) ₹36
19. 19.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 11 days (d) 17 days
20. 20.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 25 days (d) 13 days
21. 21.If 8 pens cost ₹120, how much do 12 pens cost? (a) ₹124 (b) ₹195 (c) ₹180 (d) ₹1440
22. 22.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 3 days (c) 21 days (d) 11 days
23. 23.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 12 days (d) 13 days
24. 24.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹48 (d) ₹24
25. 25.If 4 kites cost ₹32, how much do 8 kites cost? (a) ₹256 (b) ₹36 (c) ₹72 (d) ₹64
26. 26.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 9 days (d) 3 days
27. 27.If 8 pens cost ₹144, how much do 12 pens cost? (a) ₹216 (b) ₹234 (c) ₹1728 (d) ₹148
28. 28.If 9 mangoes cost ₹117, how much do 4 mangoes cost? (a) ₹112 (b) ₹468 (c) ₹65 (d) ₹52
29. 29.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 10 days (d) 16 days
30. 30.If 7 pens cost ₹140, how much do 11 pens cost? (a) ₹220 (b) ₹1540 (c) ₹240 (d) ₹144
31. 31.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹296 (b) ₹148 (c) ₹259 (d) ₹37
32. 32.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹42 (b) ₹35 (c) ₹140 (d) ₹29
33. 33.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹144 (b) ₹32 (c) ₹88 (d) ₹16
34. 34.If 9 mangoes cost ₹153, how much do 8 mangoes cost? (a) ₹152 (b) ₹153 (c) ₹1224 (d) ₹136
35. 35.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 8 days (c) 16 days (d) 28 days
36. 36.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 16 days (d) 5 days
37. 37.If 2 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹120 (b) ₹60 (c) ₹75 (d) ₹32
38. 38.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹275 (d) ₹250
39. 39.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 16 days (d) 3 days
40. 40.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹36 (b) ₹252 (c) ₹126 (d) ₹216

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