Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 294 · 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. 1.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 36 days (d) 18 days
2. 2.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹217 (d) ₹155
3. 3.If 2 kites cost ₹42, how much do 8 kites cost? (a) ₹336 (b) ₹48 (c) ₹189 (d) ₹168
4. 4.If 3 pens cost ₹27, how much do 7 pens cost? (a) ₹31 (b) ₹72 (c) ₹189 (d) ₹63
5. 5.If 8 pens cost ₹120, how much do 12 pens cost? (a) ₹1440 (b) ₹124 (c) ₹195 (d) ₹180
6. 6.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹308 (b) ₹264 (c) ₹154 (d) ₹44
7. 7.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 11 days (d) 16 days
8. 8.If 3 pens cost ₹18, how much do 10 pens cost? (a) ₹180 (b) ₹66 (c) ₹60 (d) ₹25
9. 9.If 3 pens cost ₹72, how much do 10 pens cost? (a) ₹720 (b) ₹240 (c) ₹79 (d) ₹264
10. 10.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 3 days (d) 2 days
11. 11.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 10 days (d) 4 days
12. 12.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹56 (c) ₹16 (d) ₹96
13. 13.If 3 pens cost ₹24, how much do 2 pens cost? (a) ₹24 (b) ₹48 (c) ₹23 (d) ₹16
14. 14.If 7 pens cost ₹42, how much do 5 pens cost? (a) ₹40 (b) ₹210 (c) ₹30 (d) ₹36
15. 15.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹490 (d) ₹245
16. 16.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹273 (b) ₹195 (c) ₹234 (d) ₹39
17. 17.If 7 notebooks cost ₹147, how much do 8 notebooks cost? (a) ₹1176 (b) ₹148 (c) ₹189 (d) ₹168
18. 18.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹52 (d) ₹26
19. 19.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹123 (b) ₹205 (c) ₹164 (d) ₹41
20. 20.If 2 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹144 (b) ₹81 (c) ₹24 (d) ₹72
21. 21.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 28 days (d) 1 day
22. 22.If 8 mangoes cost ₹144, how much do 2 mangoes cost? (a) ₹54 (b) ₹138 (c) ₹36 (d) ₹288
23. 23.If 6 kites cost ₹24, how much do 9 kites cost? (a) ₹40 (b) ₹216 (c) ₹36 (d) ₹27
24. 24.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹91 (b) ₹108 (c) ₹540 (d) ₹126
25. 25.If 3 pens cost ₹48, how much do 5 pens cost? (a) ₹240 (b) ₹50 (c) ₹96 (d) ₹80
26. 26.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 54 days (d) 55 days
27. 27.If 3 pens cost ₹18, how much do 2 pens cost? (a) ₹17 (b) ₹18 (c) ₹36 (d) ₹12
28. 28.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
29. 29.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹165 (b) ₹99 (c) ₹231 (d) ₹33
30. 30.If 6 pens cost ₹84, how much do 4 pens cost? (a) ₹82 (b) ₹56 (c) ₹70 (d) ₹336
31. 31.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹72 (c) ₹96 (d) ₹24
32. 32.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 6 days (d) 7 days
33. 33.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹210 (b) ₹30 (c) ₹165 (d) ₹120
34. 34.If 5 notebooks cost ₹110, how much do 2 notebooks cost? (a) ₹107 (b) ₹44 (c) ₹66 (d) ₹220
35. 35.If 8 pens cost ₹200, how much do 2 pens cost? (a) ₹50 (b) ₹194 (c) ₹75 (d) ₹400
36. 36.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹23 (d) ₹33
37. 37.If 6 kites cost ₹18, how much do 3 kites cost? (a) ₹12 (b) ₹54 (c) ₹15 (d) ₹9
38. 38.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹36 (b) ₹18 (c) ₹27 (d) ₹9
39. 39.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 14 days (d) 15 days
40. 40.If 3 kites cost ₹30, how much do 7 kites cost? (a) ₹210 (b) ₹34 (c) ₹70 (d) ₹80

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