Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 383 · 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 ₹60, how much do 11 pens cost? (a) ₹660 (b) ₹144 (c) ₹66 (d) ₹132
2. 2.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹120 (b) ₹320 (c) ₹220 (d) ₹40
3. 3.If 3 pens cost ₹54, how much do 2 pens cost? (a) ₹54 (b) ₹108 (c) ₹53 (d) ₹36
4. 4.₹432 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹336 (b) ₹216 (c) ₹96 (d) ₹48
5. 5.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹60 (b) ₹6 (c) ₹54 (d) ₹30
6. 6.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
7. 7.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹294 (c) ₹245 (d) ₹343
8. 8.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹31 (d) ₹30
9. 9.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 9 days (d) 8 days
10. 10.If 8 mangoes cost ₹144, how much do 2 mangoes cost? (a) ₹54 (b) ₹138 (c) ₹36 (d) ₹288
11. 11.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹198 (b) ₹165 (c) ₹231 (d) ₹33
12. 12.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹24 (c) ₹72 (d) ₹96
13. 13.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 11 days (d) 3 days
14. 14.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
15. 15.If 4 pens cost ₹20, how much do 3 pens cost? (a) ₹60 (b) ₹20 (c) ₹19 (d) ₹15
16. 16.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹81 (d) ₹73
17. 17.If 7 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹82 (b) ₹420 (c) ₹72 (d) ₹60
18. 18.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 28 days (d) 13 days
19. 19.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 8 days (d) 20 days
20. 20.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 13 days (d) 10 days
21. 21.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹70 (c) ₹14 (d) ₹98
22. 22.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 12 days (d) 11 days
23. 23.If 7 kites cost ₹133, how much do 8 kites cost? (a) ₹134 (b) ₹171 (c) ₹1064 (d) ₹152
24. 24.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹132 (c) ₹192 (d) ₹24
25. 25.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 1 day (d) 3 days
26. 26.If 8 notebooks cost ₹88, how much do 9 notebooks cost? (a) ₹792 (b) ₹110 (c) ₹99 (d) ₹89
27. 27.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 32 days (c) 7 days (d) 33 days
28. 28.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 15 days (d) 14 days
29. 29.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 4 days (d) 2 days
30. 30.If 4 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹220 (b) ₹55 (c) ₹66 (d) ₹45
31. 31.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 20 days (d) 11 days
32. 32.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
33. 33.If 8 notebooks cost ₹104, how much do 4 notebooks cost? (a) ₹100 (b) ₹52 (c) ₹416 (d) ₹65
34. 34.If 6 kites cost ₹42, how much do 2 kites cost? (a) ₹38 (b) ₹14 (c) ₹84 (d) ₹21
35. 35.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹19 (d) ₹76
36. 36.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹56 (d) ₹24
37. 37.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 4 days (d) 3 days
38. 38.If 5 mangoes cost ₹30, how much do 6 mangoes cost? (a) ₹31 (b) ₹42 (c) ₹180 (d) ₹36
39. 39.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 8 days (d) 6 days
40. 40.If 8 pens cost ₹176, how much do 9 pens cost? (a) ₹220 (b) ₹177 (c) ₹198 (d) ₹1584

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