Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 387 · 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 9 kites cost ₹63, how much do 5 kites cost? (a) ₹35 (b) ₹59 (c) ₹315 (d) ₹42
2. 2.If 2 kites cost ₹50, how much do 7 kites cost? (a) ₹200 (b) ₹175 (c) ₹55 (d) ₹350
3. 3.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
4. 4.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 21 days (c) 22 days (d) 11 days
5. 5.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
6. 6.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹56 (b) ₹64 (c) ₹49 (d) ₹336
7. 7.If 5 kites cost ₹75, how much do 4 kites cost? (a) ₹60 (b) ₹74 (c) ₹300 (d) ₹75
8. 8.₹180 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹135 (b) ₹45 (c) ₹90 (d) ₹180
9. 9.If 8 pens cost ₹192, how much do 12 pens cost? (a) ₹196 (b) ₹312 (c) ₹288 (d) ₹2304
10. 10.If 6 pens cost ₹90, how much do 9 pens cost? (a) ₹810 (b) ₹135 (c) ₹150 (d) ₹93
11. 11.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 20 days
12. 12.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹192 (b) ₹216 (c) ₹48 (d) ₹240
13. 13.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 9 days (d) 45 days
14. 14.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 16 days (c) 1 day (d) 13 days
15. 15.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹144 (d) ₹120
16. 16.If 8 pens cost ₹24, how much do 10 pens cost? (a) ₹240 (b) ₹26 (c) ₹33 (d) ₹30
17. 17.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 14 days (d) 4 days
18. 18.If 9 pens cost ₹117, how much do 10 pens cost? (a) ₹143 (b) ₹1170 (c) ₹118 (d) ₹130
19. 19.If 9 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹20 (b) ₹144 (c) ₹16 (d) ₹31
20. 20.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 4 days (d) 3 days
21. 21.If 8 pens cost ₹96, how much do 12 pens cost? (a) ₹1152 (b) ₹144 (c) ₹100 (d) ₹156
22. 22.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 27 days (d) 26 days
23. 23.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 3 days
24. 24.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹31 (d) ₹45
25. 25.₹294 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹126 (b) ₹42 (c) ₹168 (d) ₹147
26. 26.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹245 (b) ₹35 (c) ₹140 (d) ₹280
27. 27.If 5 pens cost ₹20, how much do 10 pens cost? (a) ₹200 (b) ₹25 (c) ₹40 (d) ₹44
28. 28.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 1 day (d) 4 days
29. 29.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹5 (d) ₹35
30. 30.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹35 (b) ₹105 (c) ₹70 (d) ₹71
31. 31.If 6 mangoes cost ₹114, how much do 7 mangoes cost? (a) ₹133 (b) ₹115 (c) ₹152 (d) ₹798
32. 32.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
33. 33.If 5 pens cost ₹35, how much do 6 pens cost? (a) ₹36 (b) ₹42 (c) ₹210 (d) ₹49
34. 34.₹598 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹299 (b) ₹46 (c) ₹368 (d) ₹230
35. 35.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 2 days (d) 7 days
36. 36.If 8 notebooks cost ₹120, how much do 10 notebooks cost? (a) ₹165 (b) ₹122 (c) ₹1200 (d) ₹150
37. 37.If 6 pens cost ₹54, how much do 4 pens cost? (a) ₹52 (b) ₹45 (c) ₹36 (d) ₹216
38. 38.₹294 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹49 (b) ₹294 (c) ₹147 (d) ₹245
39. 39.If 2 notebooks cost ₹8, how much do 11 notebooks cost? (a) ₹17 (b) ₹88 (c) ₹48 (d) ₹44
40. 40.If 6 kites cost ₹30, how much do 3 kites cost? (a) ₹15 (b) ₹20 (c) ₹90 (d) ₹27

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