Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 80 · 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. 1.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
2. 2.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹208 (b) ₹256 (c) ₹32 (d) ₹160
3. 3.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹294 (b) ₹210 (c) ₹126 (d) ₹42
4. 4.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
5. 5.If 5 notebooks cost ₹70, how much do 9 notebooks cost? (a) ₹630 (b) ₹126 (c) ₹74 (d) ₹140
6. 6.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 6 days (c) 4 days (d) 5 days
7. 7.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹69 (b) ₹68 (c) ₹17 (d) ₹85
8. 8.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹234 (c) ₹36 (d) ₹324
9. 9.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹80 (d) ₹48
10. 10.If 9 kites cost ₹99, how much do 7 kites cost? (a) ₹88 (b) ₹97 (c) ₹77 (d) ₹693
11. 11.If 6 kites cost ₹72, how much do 4 kites cost? (a) ₹60 (b) ₹288 (c) ₹48 (d) ₹70
12. 12.If 6 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹20 (b) ₹24 (c) ₹23 (d) ₹120
13. 13.If 2 kites cost ₹40, how much do 10 kites cost? (a) ₹48 (b) ₹220 (c) ₹400 (d) ₹200
14. 14.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹40 (b) ₹35 (c) ₹10 (d) ₹30
15. 15.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 24 days (d) 6 days
16. 16.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹48 (b) ₹13 (c) ₹16 (d) ₹20
17. 17.₹405 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹180 (b) ₹270 (c) ₹45 (d) ₹225
18. 18.6 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) 10 days (d) 15 days
19. 19.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹50 (b) ₹225 (c) ₹250 (d) ₹200
20. 20.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 11 days (d) 3 days
21. 21.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 3 days (d) 1 day
22. 22.If 5 notebooks cost ₹20, how much do 2 notebooks cost? (a) ₹17 (b) ₹40 (c) ₹8 (d) ₹12
23. 23.₹329 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹47 (b) ₹235 (c) ₹141 (d) ₹188
24. 24.If 4 kites cost ₹100, how much do 2 kites cost? (a) ₹98 (b) ₹50 (c) ₹75 (d) ₹200
25. 25.If 9 pens cost ₹45, how much do 10 pens cost? (a) ₹450 (b) ₹46 (c) ₹55 (d) ₹50
26. 26.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 2 days
27. 27.₹203 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹203 (b) ₹174 (c) ₹29 (d) ₹175
28. 28.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 20 days (d) 5 days
29. 29.If 2 mangoes cost ₹50, how much do 8 mangoes cost? (a) ₹56 (b) ₹225 (c) ₹200 (d) ₹400
30. 30.If 5 notebooks cost ₹25, how much do 6 notebooks cost? (a) ₹26 (b) ₹150 (c) ₹35 (d) ₹30
31. 31.₹126 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹63 (b) ₹14 (c) ₹98 (d) ₹28
32. 32.If 2 mangoes cost ₹18, how much do 8 mangoes cost? (a) ₹144 (b) ₹24 (c) ₹81 (d) ₹72
33. 33.If 3 mangoes cost ₹54, how much do 12 mangoes cost? (a) ₹63 (b) ₹648 (c) ₹216 (d) ₹234
34. 34.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 26 days (d) 10 days
35. 35.If 7 kites cost ₹98, how much do 2 kites cost? (a) ₹28 (b) ₹196 (c) ₹93 (d) ₹42
36. 36.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹49 (b) ₹196 (c) ₹245 (d) ₹147
37. 37.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 19 days (c) 11 days (d) 28 days
38. 38.If 4 kites cost ₹84, how much do 5 kites cost? (a) ₹420 (b) ₹126 (c) ₹105 (d) ₹85
39. 39.6 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) 21 days (d) 11 days
40. 40.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 22 days (d) 9 days

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