Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 522 · 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 4 kites cost ₹28, how much do 10 kites cost? (a) ₹280 (b) ₹77 (c) ₹34 (d) ₹70
2. 2.If 2 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹72 (b) ₹36 (c) ₹42 (d) ₹16
3. 3.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹147 (b) ₹98 (c) ₹49 (d) ₹196
4. 4.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹308 (d) ₹176
5. 5.8 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) 14 days (d) 7 days
6. 6.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹30 (d) ₹35
7. 7.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 7 days (c) 13 days (d) 4 days
8. 8.If 3 notebooks cost ₹9, how much do 8 notebooks cost? (a) ₹24 (b) ₹72 (c) ₹14 (d) ₹27
9. 9.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 2 days (d) 8 days
10. 10.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹42 (b) ₹54 (c) ₹30 (d) ₹6
11. 11.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 11 days
12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
13. 13.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 2 days
14. 14.If 4 mangoes cost ₹20, how much do 2 mangoes cost? (a) ₹15 (b) ₹10 (c) ₹40 (d) ₹18
15. 15.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 17 days
16. 16.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 5 days (d) 6 days
17. 17.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹30 (b) ₹210 (c) ₹135 (d) ₹60
18. 18.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹186 (b) ₹124 (c) ₹31 (d) ₹155
19. 19.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹27 (b) ₹108 (c) ₹270 (d) ₹243
20. 20.If 5 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹48 (b) ₹36 (c) ₹180 (d) ₹58
21. 21.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 15 days
22. 22.If 5 pens cost ₹25, how much do 4 pens cost? (a) ₹20 (b) ₹24 (c) ₹100 (d) ₹25
23. 23.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 19 days (d) 11 days
24. 24.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹12 (d) ₹18
25. 25.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹79 (c) ₹13 (d) ₹78
26. 26.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 18 days (d) 3 days
27. 27.If 7 pens cost ₹98, how much do 11 pens cost? (a) ₹102 (b) ₹1078 (c) ₹168 (d) ₹154
28. 28.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹144 (b) ₹88 (c) ₹32 (d) ₹16
29. 29.₹320 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹288 (b) ₹320 (c) ₹32 (d) ₹160
30. 30.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 12 days (d) 9 days
31. 31.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 15 days (d) 27 days
32. 32.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 6 days (d) 4 days
33. 33.₹480 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹48 (b) ₹432 (c) ₹240 (d) ₹480
34. 34.If 3 pens cost ₹18, how much do 11 pens cost? (a) ₹198 (b) ₹72 (c) ₹26 (d) ₹66
35. 35.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹234 (b) ₹273 (c) ₹195 (d) ₹39
36. 36.If 2 kites cost ₹38, how much do 5 kites cost? (a) ₹41 (b) ₹190 (c) ₹114 (d) ₹95
37. 37.If 2 mangoes cost ₹22, how much do 9 mangoes cost? (a) ₹198 (b) ₹110 (c) ₹99 (d) ₹29
38. 38.If 6 kites cost ₹30, how much do 2 kites cost? (a) ₹26 (b) ₹60 (c) ₹15 (d) ₹10
39. 39.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹352 (b) ₹44 (c) ₹286 (d) ₹220
40. 40.If 4 pens cost ₹36, how much do 8 pens cost? (a) ₹81 (b) ₹288 (c) ₹72 (d) ₹40

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