Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 434 · 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.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹182 (b) ₹130 (c) ₹26 (d) ₹156
2. 2.₹450 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹135 (b) ₹315 (c) ₹225 (d) ₹45
3. 3.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 7 days (c) 17 days (d) 6 days
4. 4.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 21 days (d) 1 day
5. 5.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹154 (b) ₹99 (c) ₹44 (d) ₹22
6. 6.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹162 (b) ₹135 (c) ₹189 (d) ₹27
7. 7.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 20 days (c) 6 days (d) 5 days
8. 8.If 7 kites cost ₹154, how much do 3 kites cost? (a) ₹150 (b) ₹462 (c) ₹88 (d) ₹66
9. 9.If 9 kites cost ₹189, how much do 2 kites cost? (a) ₹182 (b) ₹378 (c) ₹63 (d) ₹42
10. 10.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 17 days (d) 16 days
11. 11.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹119 (d) ₹136
12. 12.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹19 (b) ₹76 (c) ₹114 (d) ₹95
13. 13.If 3 pens cost ₹45, how much do 12 pens cost? (a) ₹195 (b) ₹180 (c) ₹54 (d) ₹540
14. 14.If 6 kites cost ₹48, how much do 11 kites cost? (a) ₹88 (b) ₹53 (c) ₹528 (d) ₹96
15. 15.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹210 (d) ₹231
16. 16.If 4 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹126 (b) ₹420 (c) ₹85 (d) ₹105
17. 17.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹110 (b) ₹99 (c) ₹44 (d) ₹11
18. 18.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹153 (b) ₹238 (c) ₹68 (d) ₹34
19. 19.If 6 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹52 (b) ₹30 (c) ₹288 (d) ₹48
20. 20.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹30 (d) ₹75
21. 21.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹77 (d) ₹11
22. 22.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 2 days (d) 19 days
23. 23.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 5 days (d) 13 days
24. 24.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
25. 25.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 53 days (c) 19 days (d) 52 days
26. 26.If 6 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹32 (b) ₹26 (c) ₹36 (d) ₹192
27. 27.₹297 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹264 (b) ₹265 (c) ₹33 (d) ₹297
28. 28.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 14 days (d) 13 days
29. 29.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹10 (d) ₹5
30. 30.If 4 pens cost ₹72, how much do 2 pens cost? (a) ₹70 (b) ₹54 (c) ₹144 (d) ₹36
31. 31.If 8 pens cost ₹152, how much do 9 pens cost? (a) ₹171 (b) ₹153 (c) ₹1368 (d) ₹190
32. 32.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹72 (d) ₹64
33. 33.If 2 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹96 (b) ₹29 (c) ₹84 (d) ₹168
34. 34.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 8 days
35. 35.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹24 (b) ₹27 (c) ₹30 (d) ₹6
36. 36.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹16 (b) ₹128 (c) ₹48 (d) ₹88
37. 37.If 7 mangoes cost ₹56, how much do 12 mangoes cost? (a) ₹96 (b) ₹104 (c) ₹672 (d) ₹61
38. 38.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 15 days (d) 11 days
39. 39.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹18 (d) ₹24
40. 40.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 43 days (c) 7 days (d) 42 days

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