Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 735 · 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.If 9 pens cost ₹162, how much do 3 pens cost? (a) ₹72 (b) ₹486 (c) ₹156 (d) ₹54
2. 2.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 2 days
3. 3.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹78 (b) ₹48 (c) ₹108 (d) ₹12
4. 4.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹90 (d) ₹75
5. 5.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 19 days (d) 11 days
6. 6.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 39 days (c) 40 days (d) 7 days
7. 7.If 2 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹432 (b) ₹234 (c) ₹46 (d) ₹216
8. 8.If 5 kites cost ₹45, how much do 4 kites cost? (a) ₹44 (b) ₹180 (c) ₹45 (d) ₹36
9. 9.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹54 (d) ₹55
10. 10.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 8 days (d) 16 days
11. 11.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 1 day (d) 17 days
12. 12.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 18 days (d) 7 days
13. 13.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
14. 14.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹90 (d) ₹150
15. 15.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 10 days
16. 16.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹132 (b) ₹34 (c) ₹55 (d) ₹44
17. 17.If 8 notebooks cost ₹80, how much do 11 notebooks cost? (a) ₹83 (b) ₹880 (c) ₹110 (d) ₹120
18. 18.If 9 mangoes cost ₹36, how much do 5 mangoes cost? (a) ₹20 (b) ₹180 (c) ₹24 (d) ₹32
19. 19.If 3 kites cost ₹63, how much do 4 kites cost? (a) ₹64 (b) ₹84 (c) ₹252 (d) ₹105
20. 20.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 27 days (d) 13 days
21. 21.If 6 notebooks cost ₹108, how much do 10 notebooks cost? (a) ₹112 (b) ₹1080 (c) ₹198 (d) ₹180
22. 22.If 6 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹53 (b) ₹528 (c) ₹88 (d) ₹96
23. 23.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹105 (c) ₹120 (d) ₹90
24. 24.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹297 (d) ₹264
25. 25.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 1 day (d) 2 days
26. 26.If 8 pens cost ₹120, how much do 4 pens cost? (a) ₹116 (b) ₹75 (c) ₹60 (d) ₹480
27. 27.If 8 notebooks cost ₹184, how much do 10 notebooks cost? (a) ₹186 (b) ₹253 (c) ₹1840 (d) ₹230
28. 28.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹108 (b) ₹12 (c) ₹60 (d) ₹84
29. 29.If 3 pens cost ₹24, how much do 11 pens cost? (a) ₹96 (b) ₹32 (c) ₹88 (d) ₹264
30. 30.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 9 days (d) 10 days
31. 31.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 10 days (d) 17 days
32. 32.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 17 days (d) 8 days
33. 33.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹81 (c) ₹18 (d) ₹9
34. 34.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹245 (d) ₹196
35. 35.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 25 days (c) 4 days (d) 13 days
36. 36.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹99 (b) ₹67 (c) ₹33 (d) ₹66
37. 37.If 9 notebooks cost ₹27, how much do 11 notebooks cost? (a) ₹36 (b) ₹29 (c) ₹297 (d) ₹33
38. 38.If 5 kites cost ₹90, how much do 9 kites cost? (a) ₹180 (b) ₹94 (c) ₹162 (d) ₹810
39. 39.If 3 mangoes cost ₹45, how much do 11 mangoes cost? (a) ₹53 (b) ₹180 (c) ₹495 (d) ₹165
40. 40.If 2 mangoes cost ₹14, how much do 7 mangoes cost? (a) ₹19 (b) ₹56 (c) ₹98 (d) ₹49

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