Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 676 · 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 3 mangoes cost ₹75, how much do 4 mangoes cost? (a) ₹125 (b) ₹76 (c) ₹300 (d) ₹100
2. 2.If 2 notebooks cost ₹30, how much do 12 notebooks cost? (a) ₹360 (b) ₹180 (c) ₹195 (d) ₹40
3. 3.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 15 days (d) 3 days
4. 4.If 6 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹840 (b) ₹121 (c) ₹140 (d) ₹160
5. 5.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹88 (b) ₹99 (c) ₹89 (d) ₹11
6. 6.5 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
7. 7.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹333 (b) ₹296 (c) ₹37 (d) ₹111
8. 8.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹24 (d) ₹6
9. 9.If 4 kites cost ₹32, how much do 5 kites cost? (a) ₹48 (b) ₹40 (c) ₹33 (d) ₹160
10. 10.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹140 (b) ₹175 (c) ₹35 (d) ₹105
11. 11.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 21 days (d) 45 days
12. 12.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 1 day (d) 3 days
13. 13.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹169 (c) ₹26 (d) ₹104
14. 14.If 3 kites cost ₹69, how much do 11 kites cost? (a) ₹77 (b) ₹276 (c) ₹253 (d) ₹759
15. 15.If 6 notebooks cost ₹66, how much do 3 notebooks cost? (a) ₹198 (b) ₹33 (c) ₹44 (d) ₹63
16. 16.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 25 days (d) 9 days
17. 17.If 7 kites cost ₹28, how much do 6 kites cost? (a) ₹28 (b) ₹24 (c) ₹27 (d) ₹168
18. 18.If 6 pens cost ₹114, how much do 7 pens cost? (a) ₹152 (b) ₹115 (c) ₹133 (d) ₹798
19. 19.If 6 mangoes cost ₹120, how much do 2 mangoes cost? (a) ₹60 (b) ₹40 (c) ₹240 (d) ₹116
20. 20.If 9 mangoes cost ₹63, how much do 10 mangoes cost? (a) ₹64 (b) ₹70 (c) ₹77 (d) ₹630
21. 21.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹42 (b) ₹49 (c) ₹56 (d) ₹14
22. 22.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 5 days (d) 45 days
23. 23.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹11 (d) ₹33
24. 24.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 11 days (d) 21 days
25. 25.If 8 pens cost ₹56, how much do 12 pens cost? (a) ₹91 (b) ₹672 (c) ₹60 (d) ₹84
26. 26.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹72 (c) ₹16 (d) ₹128
27. 27.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹144 (d) ₹336
28. 28.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 1 day
29. 29.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹48 (d) ₹80
30. 30.₹210 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹147 (d) ₹105
31. 31.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹160 (c) ₹220 (d) ₹280
32. 32.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹24 (d) ₹42
33. 33.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 8 days (d) 36 days
34. 34.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 7 days
35. 35.If 2 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹150 (b) ₹37 (c) ₹270 (d) ₹135
36. 36.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 18 days (d) 14 days
37. 37.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 29 days (d) 28 days
38. 38.If 6 notebooks cost ₹72, how much do 4 notebooks cost? (a) ₹288 (b) ₹70 (c) ₹48 (d) ₹60
39. 39.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 2 days (d) 8 days
40. 40.If 8 notebooks cost ₹176, how much do 9 notebooks cost? (a) ₹220 (b) ₹1584 (c) ₹177 (d) ₹198

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