Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 55 · 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.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹150 (b) ₹175 (c) ₹125 (d) ₹25
2. 2.If 3 notebooks cost ₹21, how much do 2 notebooks cost? (a) ₹42 (b) ₹14 (c) ₹20 (d) ₹21
3. 3.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹36 (d) ₹27
4. 4.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 17 days (d) 21 days
5. 5.If 5 kites cost ₹125, how much do 9 kites cost? (a) ₹1125 (b) ₹129 (c) ₹250 (d) ₹225
6. 6.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹65 (b) ₹90 (c) ₹10 (d) ₹40
7. 7.₹324 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹189 (b) ₹162 (c) ₹135 (d) ₹27
8. 8.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹161 (d) ₹92
9. 9.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 19 days (d) 9 days
10. 10.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 13 days (d) 25 days
11. 11.₹141 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹47 (b) ₹141 (c) ₹94 (d) ₹95
12. 12.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 11 days (d) 19 days
13. 13.If 8 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹24 (b) ₹43 (c) ₹18 (d) ₹144
14. 14.If 4 pens cost ₹32, how much do 2 pens cost? (a) ₹30 (b) ₹24 (c) ₹16 (d) ₹64
15. 15.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹216 (b) ₹24 (c) ₹168 (d) ₹120
16. 16.If 3 kites cost ₹51, how much do 9 kites cost? (a) ₹459 (b) ₹153 (c) ₹170 (d) ₹57
17. 17.If 2 notebooks cost ₹38, how much do 12 notebooks cost? (a) ₹48 (b) ₹247 (c) ₹456 (d) ₹228
18. 18.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 13 days (d) 10 days
19. 19.If 4 kites cost ₹92, how much do 6 kites cost? (a) ₹552 (b) ₹94 (c) ₹138 (d) ₹161
20. 20.If 6 kites cost ₹108, how much do 2 kites cost? (a) ₹104 (b) ₹54 (c) ₹216 (d) ₹36
21. 21.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹132 (b) ₹264 (c) ₹33 (d) ₹231
22. 22.If 2 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹19 (b) ₹40 (c) ₹80 (d) ₹48
23. 23.If 7 notebooks cost ₹49, how much do 3 notebooks cost? (a) ₹45 (b) ₹28 (c) ₹21 (d) ₹147
24. 24.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 16 days (c) 4 days (d) 8 days
25. 25.If 9 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹60 (b) ₹55 (c) ₹66 (d) ₹540
26. 26.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹15 (b) ₹12 (c) ₹108 (d) ₹22
27. 27.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 34 days (c) 33 days (d) 15 days
28. 28.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹209 (b) ₹152 (c) ₹266 (d) ₹38
29. 29.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹165 (b) ₹231 (c) ₹33 (d) ₹297
30. 30.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 17 days (d) 13 days
31. 31.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹24 (b) ₹156 (c) ₹120 (d) ₹192
32. 32.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹25 (b) ₹50 (c) ₹100 (d) ₹75
33. 33.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹195 (b) ₹234 (c) ₹156 (d) ₹39
34. 34.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 12 days (d) 4 days
35. 35.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹104 (d) ₹91
36. 36.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹72 (d) ₹42
37. 37.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹42 (b) ₹168 (c) ₹378 (d) ₹273
38. 38.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹264 (b) ₹308 (c) ₹220 (d) ₹44
39. 39.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹190 (b) ₹228 (c) ₹114 (d) ₹38
40. 40.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 14 days (d) 5 days

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