Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 744 · 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.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹253 (b) ₹184 (c) ₹46 (d) ₹322
2. 2.If 6 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹24 (b) ₹126 (c) ₹19 (d) ₹21
3. 3.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 9 days
4. 4.If 8 pens cost ₹96, how much do 3 pens cost? (a) ₹36 (b) ₹91 (c) ₹48 (d) ₹288
5. 5.If 3 pens cost ₹66, how much do 12 pens cost? (a) ₹792 (b) ₹264 (c) ₹286 (d) ₹75
6. 6.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹196 (b) ₹245 (c) ₹147 (d) ₹49
7. 7.If 8 kites cost ₹184, how much do 11 kites cost? (a) ₹253 (b) ₹187 (c) ₹2024 (d) ₹276
8. 8.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹225 (b) ₹270 (c) ₹90 (d) ₹45
9. 9.If 6 mangoes cost ₹30, how much do 7 mangoes cost? (a) ₹31 (b) ₹35 (c) ₹40 (d) ₹210
10. 10.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹44 (b) ₹45 (c) ₹55 (d) ₹11
11. 11.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹88 (b) ₹11 (c) ₹77 (d) ₹44
12. 12.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹91 (b) ₹288 (c) ₹36 (d) ₹48
13. 13.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹308 (b) ₹220 (c) ₹44 (d) ₹264
14. 14.If 6 pens cost ₹90, how much do 3 pens cost? (a) ₹45 (b) ₹87 (c) ₹270 (d) ₹60
15. 15.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹320 (b) ₹180 (c) ₹40 (d) ₹360
16. 16.If 3 mangoes cost ₹48, how much do 2 mangoes cost? (a) ₹96 (b) ₹47 (c) ₹48 (d) ₹32
17. 17.If 3 pens cost ₹36, how much do 4 pens cost? (a) ₹144 (b) ₹37 (c) ₹48 (d) ₹60
18. 18.₹182 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹26 (b) ₹182 (c) ₹156 (d) ₹91
19. 19.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹111 (b) ₹148 (c) ₹37 (d) ₹185
20. 20.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹287 (d) ₹123
21. 21.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
22. 22.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 9 days
23. 23.If 3 notebooks cost ₹27, how much do 7 notebooks cost? (a) ₹63 (b) ₹189 (c) ₹31 (d) ₹72
24. 24.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹450 (b) ₹45 (c) ₹225 (d) ₹405
25. 25.₹418 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹152 (b) ₹209 (c) ₹38 (d) ₹266
26. 26.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 17 days
27. 27.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 25 days (d) 24 days
28. 28.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹28 (b) ₹58 (c) ₹252 (d) ₹35
29. 29.If 5 pens cost ₹115, how much do 7 pens cost? (a) ₹184 (b) ₹161 (c) ₹805 (d) ₹117
30. 30.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
31. 31.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 8 days (d) 18 days
32. 32.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 27 days (d) 17 days
33. 33.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 17 days (d) 13 days
34. 34.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹70 (c) ₹84 (d) ₹14
35. 35.If 2 mangoes cost ₹30, how much do 7 mangoes cost? (a) ₹35 (b) ₹105 (c) ₹120 (d) ₹210
36. 36.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 12 days (d) 28 days
37. 37.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹240 (b) ₹264 (c) ₹288 (d) ₹48
38. 38.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 4 days (d) 3 days
39. 39.₹380 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹266 (b) ₹190 (c) ₹114 (d) ₹38
40. 40.If 4 kites cost ₹68, how much do 11 kites cost? (a) ₹75 (b) ₹204 (c) ₹748 (d) ₹187

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