Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 686 · 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 6 pens cost ₹18, how much do 3 pens cost? (a) ₹12 (b) ₹15 (c) ₹54 (d) ₹9
2. 2.If 2 mangoes cost ₹6, how much do 7 mangoes cost? (a) ₹42 (b) ₹11 (c) ₹24 (d) ₹21
3. 3.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹196 (d) ₹252
4. 4.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 12 days (c) 5 days (d) 7 days
5. 5.If 5 mangoes cost ₹125, how much do 11 mangoes cost? (a) ₹1375 (b) ₹275 (c) ₹131 (d) ₹300
6. 6.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 18 days (d) 11 days
7. 7.If 9 kites cost ₹99, how much do 12 kites cost? (a) ₹132 (b) ₹143 (c) ₹102 (d) ₹1188
8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 17 days (d) 13 days
9. 9.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹132 (c) ₹165 (d) ₹99
10. 10.If 5 pens cost ₹35, how much do 8 pens cost? (a) ₹280 (b) ₹63 (c) ₹38 (d) ₹56
11. 11.₹350 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹245 (b) ₹105 (c) ₹35 (d) ₹175
12. 12.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹66 (d) ₹132
13. 13.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
14. 14.If 8 notebooks cost ₹56, how much do 7 notebooks cost? (a) ₹56 (b) ₹392 (c) ₹49 (d) ₹55
15. 15.If 8 notebooks cost ₹152, how much do 10 notebooks cost? (a) ₹209 (b) ₹1520 (c) ₹190 (d) ₹154
16. 16.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹184 (b) ₹23 (c) ₹92 (d) ₹161
17. 17.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
18. 18.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹141 (c) ₹47 (d) ₹329
19. 19.If 4 kites cost ₹100, how much do 9 kites cost? (a) ₹105 (b) ₹900 (c) ₹225 (d) ₹250
20. 20.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹246 (b) ₹205 (c) ₹82 (d) ₹41
21. 21.If 9 notebooks cost ₹198, how much do 8 notebooks cost? (a) ₹198 (b) ₹176 (c) ₹1584 (d) ₹197
22. 22.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹40 (c) ₹10 (d) ₹25
23. 23.If 7 pens cost ₹105, how much do 10 pens cost? (a) ₹1050 (b) ₹150 (c) ₹108 (d) ₹165
24. 24.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 3 days (d) 4 days
25. 25.If 8 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹144 (b) ₹143 (c) ₹1008 (d) ₹126
26. 26.If 5 notebooks cost ₹45, how much do 9 notebooks cost? (a) ₹90 (b) ₹81 (c) ₹405 (d) ₹49
27. 27.If 3 pens cost ₹54, how much do 5 pens cost? (a) ₹56 (b) ₹90 (c) ₹108 (d) ₹270
28. 28.If 3 notebooks cost ₹57, how much do 2 notebooks cost? (a) ₹114 (b) ₹38 (c) ₹56 (d) ₹57
29. 29.If 9 mangoes cost ₹216, how much do 10 mangoes cost? (a) ₹264 (b) ₹217 (c) ₹2160 (d) ₹240
30. 30.If 6 kites cost ₹120, how much do 7 kites cost? (a) ₹121 (b) ₹140 (c) ₹840 (d) ₹160
31. 31.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 17 days (d) 4 days
32. 32.₹495 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹360 (b) ₹45 (c) ₹135 (d) ₹405
33. 33.If 7 kites cost ₹70, how much do 11 kites cost? (a) ₹770 (b) ₹110 (c) ₹120 (d) ₹74
34. 34.3 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) 18 days (d) 2 days
35. 35.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 18 days (c) 16 days (d) 9 days
36. 36.If 4 pens cost ₹52, how much do 5 pens cost? (a) ₹78 (b) ₹65 (c) ₹53 (d) ₹260
37. 37.If 2 mangoes cost ₹30, how much do 12 mangoes cost? (a) ₹40 (b) ₹180 (c) ₹195 (d) ₹360
38. 38.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹138 (b) ₹184 (c) ₹161 (d) ₹46
39. 39.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹93 (d) ₹92
40. 40.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 26 days (c) 15 days (d) 27 days

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