Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 878 · 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.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹36 (c) ₹108 (d) ₹72
2. 2.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹55 (b) ₹99 (c) ₹110 (d) ₹11
3. 3.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹105 (c) ₹140 (d) ₹35
4. 4.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 14 days (d) 22 days
5. 5.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹33 (d) ₹22
6. 6.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 36 days (d) 4 days
7. 7.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 14 days (d) 9 days
8. 8.If 7 pens cost ₹175, how much do 6 pens cost? (a) ₹174 (b) ₹1050 (c) ₹175 (d) ₹150
9. 9.If 8 kites cost ₹112, how much do 12 kites cost? (a) ₹116 (b) ₹1344 (c) ₹182 (d) ₹168
10. 10.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 12 days (d) 7 days
11. 11.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹11 (c) ₹15 (d) ₹5
12. 12.If 7 notebooks cost ₹21, how much do 4 notebooks cost? (a) ₹84 (b) ₹12 (c) ₹15 (d) ₹18
13. 13.If 4 kites cost ₹64, how much do 3 kites cost? (a) ₹192 (b) ₹64 (c) ₹48 (d) ₹63
14. 14.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 6 days (d) 9 days
15. 15.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹56 (d) ₹49
16. 16.If 3 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹210 (b) ₹34 (c) ₹70 (d) ₹80
17. 17.₹297 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹231 (b) ₹66 (c) ₹33 (d) ₹264
18. 18.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 1 day (d) 9 days
19. 19.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹325 (d) ₹400
20. 20.If 8 notebooks cost ₹160, how much do 2 notebooks cost? (a) ₹154 (b) ₹320 (c) ₹60 (d) ₹40
21. 21.₹517 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹47 (b) ₹141 (c) ₹376 (d) ₹423
22. 22.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹261 (d) ₹145
23. 23.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 12 days (d) 8 days
24. 24.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 8 days (c) 57 days (d) 56 days
25. 25.If 6 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹96 (b) ₹432 (c) ₹72 (d) ₹141
26. 26.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days
27. 27.If 6 kites cost ₹36, how much do 10 kites cost? (a) ₹66 (b) ₹60 (c) ₹360 (d) ₹40
28. 28.₹330 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹165 (b) ₹240 (c) ₹30 (d) ₹90
29. 29.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
30. 30.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
31. 31.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹68 (d) ₹17
32. 32.If 8 mangoes cost ₹200, how much do 10 mangoes cost? (a) ₹202 (b) ₹250 (c) ₹2000 (d) ₹275
33. 33.If 4 kites cost ₹100, how much do 2 kites cost? (a) ₹98 (b) ₹50 (c) ₹200 (d) ₹75
34. 34.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 7 days (d) 4 days
35. 35.If 9 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹103 (b) ₹60 (c) ₹48 (d) ₹432
36. 36.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹35 (d) ₹105
37. 37.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 8 days (d) 17 days
38. 38.If 6 mangoes cost ₹66, how much do 7 mangoes cost? (a) ₹88 (b) ₹77 (c) ₹67 (d) ₹462
39. 39.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹184 (b) ₹138 (c) ₹46 (d) ₹92
40. 40.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹46 (b) ₹276 (c) ₹253 (d) ₹230

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