Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 671 · 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 5 pens cost ₹80, how much do 6 pens cost? (a) ₹112 (b) ₹480 (c) ₹96 (d) ₹81
2. 2.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 10 days (c) 40 days (d) 41 days
3. 3.If 7 pens cost ₹98, how much do 2 pens cost? (a) ₹196 (b) ₹42 (c) ₹93 (d) ₹28
4. 4.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹150 (b) ₹180 (c) ₹210 (d) ₹30
5. 5.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
6. 6.If 3 kites cost ₹54, how much do 7 kites cost? (a) ₹126 (b) ₹144 (c) ₹378 (d) ₹58
7. 7.If 6 mangoes cost ₹108, how much do 9 mangoes cost? (a) ₹180 (b) ₹972 (c) ₹162 (d) ₹111
8. 8.₹216 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹180 (d) ₹216
9. 9.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹312 (b) ₹273 (c) ₹78 (d) ₹39
10. 10.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹259 (b) ₹185 (c) ₹222 (d) ₹37
11. 11.If 9 kites cost ₹189, how much do 10 kites cost? (a) ₹1890 (b) ₹231 (c) ₹190 (d) ₹210
12. 12.If 9 mangoes cost ₹216, how much do 8 mangoes cost? (a) ₹215 (b) ₹192 (c) ₹1728 (d) ₹216
13. 13.₹217 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹187 (d) ₹186
14. 14.If 9 pens cost ₹63, how much do 5 pens cost? (a) ₹59 (b) ₹42 (c) ₹35 (d) ₹315
15. 15.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹84 (d) ₹85
16. 16.If 2 pens cost ₹10, how much do 5 pens cost? (a) ₹30 (b) ₹50 (c) ₹25 (d) ₹13
17. 17.If 9 pens cost ₹189, how much do 6 pens cost? (a) ₹1134 (b) ₹126 (c) ₹186 (d) ₹147
18. 18.If 7 pens cost ₹49, how much do 9 pens cost? (a) ₹63 (b) ₹70 (c) ₹441 (d) ₹51
19. 19.₹175 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹150 (b) ₹151 (c) ₹175 (d) ₹25
20. 20.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹16 (d) ₹20
21. 21.If 9 pens cost ₹117, how much do 2 pens cost? (a) ₹26 (b) ₹39 (c) ₹110 (d) ₹234
22. 22.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹176 (b) ₹198 (c) ₹44 (d) ₹220
23. 23.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹30 (b) ₹270 (c) ₹120 (d) ₹195
24. 24.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 1 day
25. 25.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹108 (b) ₹60 (c) ₹84 (d) ₹12
26. 26.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹60 (b) ₹78 (c) ₹12 (d) ₹96
27. 27.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹180 (d) ₹110
28. 28.If 9 kites cost ₹225, how much do 11 kites cost? (a) ₹275 (b) ₹300 (c) ₹227 (d) ₹2475
29. 29.If 7 pens cost ₹105, how much do 2 pens cost? (a) ₹30 (b) ₹100 (c) ₹45 (d) ₹210
30. 30.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹48 (d) ₹36
31. 31.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹45 (d) ₹25
32. 32.If 7 mangoes cost ₹63, how much do 9 mangoes cost? (a) ₹567 (b) ₹65 (c) ₹81 (d) ₹90
33. 33.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹10 (b) ₹5 (c) ₹20 (d) ₹15
34. 34.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 16 days (d) 7 days
35. 35.If 6 pens cost ₹78, how much do 3 pens cost? (a) ₹39 (b) ₹234 (c) ₹75 (d) ₹52
36. 36.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹58 (d) ₹116
37. 37.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹24 (b) ₹48 (c) ₹6 (d) ₹42
38. 38.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹88 (d) ₹66
39. 39.If 4 pens cost ₹100, how much do 9 pens cost? (a) ₹105 (b) ₹250 (c) ₹225 (d) ₹900
40. 40.If 3 mangoes cost ₹27, how much do 4 mangoes cost? (a) ₹36 (b) ₹108 (c) ₹28 (d) ₹45

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