Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 699 · 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 2 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹99 (b) ₹198 (c) ₹27 (d) ₹108
2. 2.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 48 days (c) 6 days (d) 3 days
3. 3.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹16 (b) ₹48 (c) ₹80 (d) ₹112
4. 4.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 4 days (d) 11 days
5. 5.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹162 (b) ₹72 (c) ₹252 (d) ₹36
6. 6.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹73 (d) ₹9
7. 7.If 7 kites cost ₹168, how much do 8 kites cost? (a) ₹1344 (b) ₹192 (c) ₹169 (d) ₹216
8. 8.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 36 days (c) 18 days (d) 4 days
9. 9.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 9 days (c) 27 days (d) 17 days
10. 10.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹215 (d) ₹172
11. 11.If 5 kites cost ₹110, how much do 3 kites cost? (a) ₹66 (b) ₹330 (c) ₹88 (d) ₹108
12. 12.If 8 mangoes cost ₹120, how much do 12 mangoes cost? (a) ₹124 (b) ₹1440 (c) ₹180 (d) ₹195
13. 13.If 9 kites cost ₹27, how much do 10 kites cost? (a) ₹33 (b) ₹30 (c) ₹270 (d) ₹28
14. 14.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹25 (b) ₹20 (c) ₹60 (d) ₹16
15. 15.If 5 notebooks cost ₹75, how much do 4 notebooks cost? (a) ₹60 (b) ₹74 (c) ₹300 (d) ₹75
16. 16.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 11 days (c) 15 days (d) 27 days
17. 17.₹66 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹44 (d) ₹33
18. 18.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹21 (b) ₹84 (c) ₹63 (d) ₹105
19. 19.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 12 days (d) 8 days
20. 20.If 4 pens cost ₹44, how much do 11 pens cost? (a) ₹121 (b) ₹51 (c) ₹132 (d) ₹484
21. 21.₹250 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹75 (b) ₹125 (c) ₹25 (d) ₹175
22. 22.If 7 mangoes cost ₹63, how much do 8 mangoes cost? (a) ₹72 (b) ₹504 (c) ₹81 (d) ₹64
23. 23.If 4 mangoes cost ₹92, how much do 9 mangoes cost? (a) ₹230 (b) ₹97 (c) ₹207 (d) ₹828
24. 24.₹189 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹169 (b) ₹168 (c) ₹189 (d) ₹21
25. 25.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 14 days (d) 3 days
26. 26.If 5 kites cost ₹85, how much do 8 kites cost? (a) ₹88 (b) ₹153 (c) ₹680 (d) ₹136
27. 27.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹91 (d) ₹65
28. 28.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹147 (d) ₹196
29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 4 days (d) 2 days
30. 30.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹45 (c) ₹54 (d) ₹9
31. 31.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 17 days (d) 16 days
32. 32.If 9 pens cost ₹54, how much do 8 pens cost? (a) ₹54 (b) ₹53 (c) ₹48 (d) ₹432
33. 33.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹11 (b) ₹99 (c) ₹110 (d) ₹55
34. 34.If 6 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹30 (b) ₹144 (c) ₹24 (d) ₹34
35. 35.₹460 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹414 (d) ₹460
36. 36.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹51 (d) ₹68
37. 37.If 3 pens cost ₹39, how much do 2 pens cost? (a) ₹26 (b) ₹38 (c) ₹39 (d) ₹78
38. 38.If 6 pens cost ₹48, how much do 2 pens cost? (a) ₹24 (b) ₹16 (c) ₹44 (d) ₹96
39. 39.If 5 mangoes cost ₹20, how much do 4 mangoes cost? (a) ₹80 (b) ₹16 (c) ₹20 (d) ₹19
40. 40.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 14 days (d) 11 days

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