Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 804 · 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. 1.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 5 days (d) 16 days
2. 2.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 16 days (d) 10 days
3. 3.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹37 (b) ₹296 (c) ₹148 (d) ₹259
4. 4.If 9 pens cost ₹180, how much do 2 pens cost? (a) ₹40 (b) ₹173 (c) ₹360 (d) ₹60
5. 5.If 7 notebooks cost ₹98, how much do 3 notebooks cost? (a) ₹56 (b) ₹42 (c) ₹294 (d) ₹94
6. 6.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 27 days (d) 11 days
7. 7.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 15 days (d) 10 days
8. 8.If 7 notebooks cost ₹63, how much do 8 notebooks cost? (a) ₹81 (b) ₹64 (c) ₹504 (d) ₹72
9. 9.If 8 mangoes cost ₹136, how much do 3 mangoes cost? (a) ₹68 (b) ₹408 (c) ₹51 (d) ₹131
10. 10.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹308 (b) ₹44 (c) ₹264 (d) ₹220
11. 11.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹8 (c) ₹20 (d) ₹16
12. 12.₹352 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹176 (d) ₹220
13. 13.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 2 days (d) 11 days
14. 14.If 5 notebooks cost ₹25, how much do 8 notebooks cost? (a) ₹45 (b) ₹200 (c) ₹40 (d) ₹28
15. 15.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 6 days (d) 24 days
16. 16.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹8 (b) ₹32 (c) ₹40 (d) ₹36
17. 17.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹48 (b) ₹16 (c) ₹15 (d) ₹12
18. 18.If 7 kites cost ₹126, how much do 4 kites cost? (a) ₹90 (b) ₹72 (c) ₹123 (d) ₹504
19. 19.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹172 (d) ₹173
20. 20.If 2 notebooks cost ₹8, how much do 11 notebooks cost? (a) ₹88 (b) ₹17 (c) ₹44 (d) ₹48
21. 21.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 55 days (b) 5 days (c) 19 days (d) 54 days
22. 22.If 9 kites cost ₹198, how much do 2 kites cost? (a) ₹191 (b) ₹396 (c) ₹66 (d) ₹44
23. 23.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹65 (b) ₹53 (c) ₹13 (d) ₹52
24. 24.If 4 mangoes cost ₹68, how much do 5 mangoes cost? (a) ₹102 (b) ₹85 (c) ₹69 (d) ₹340
25. 25.If 2 pens cost ₹48, how much do 4 pens cost? (a) ₹120 (b) ₹192 (c) ₹96 (d) ₹50
26. 26.If 8 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹280 (b) ₹35 (c) ₹53 (d) ₹42
27. 27.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 36 days (d) 35 days
28. 28.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹60 (d) ₹84
29. 29.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
30. 30.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹155 (b) ₹93 (c) ₹124 (d) ₹31
31. 31.If 6 mangoes cost ₹102, how much do 7 mangoes cost? (a) ₹714 (b) ₹136 (c) ₹103 (d) ₹119
32. 32.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹276 (d) ₹322
33. 33.If 2 pens cost ₹44, how much do 6 pens cost? (a) ₹132 (b) ₹154 (c) ₹48 (d) ₹264
34. 34.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹174 (d) ₹175
35. 35.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 13 days (d) 7 days
36. 36.If 4 kites cost ₹100, how much do 5 kites cost? (a) ₹150 (b) ₹125 (c) ₹101 (d) ₹500
37. 37.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 4 days
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
39. 39.If 5 kites cost ₹100, how much do 6 kites cost? (a) ₹140 (b) ₹120 (c) ₹600 (d) ₹101
40. 40.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days

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