Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 263 · 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 2 kites cost ₹32, how much do 9 kites cost? (a) ₹288 (b) ₹39 (c) ₹160 (d) ₹144
2. 2.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 3 days (d) 11 days
3. 3.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 10 days
4. 4.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹35 (c) ₹50 (d) ₹20
5. 5.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 10 days
6. 6.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹328 (b) ₹369 (c) ₹205 (d) ₹41
7. 7.₹240 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹144 (b) ₹120 (c) ₹96 (d) ₹48
8. 8.₹70 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹14 (b) ₹35 (c) ₹56 (d) ₹70
9. 9.₹205 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹41 (b) ₹123 (c) ₹82 (d) ₹164
10. 10.₹270 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹135 (d) ₹225
11. 11.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 11 days (d) 10 days
12. 12.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 9 days (d) 12 days
13. 13.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹186 (b) ₹31 (c) ₹155 (d) ₹62
14. 14.If 5 pens cost ₹120, how much do 6 pens cost? (a) ₹720 (b) ₹144 (c) ₹121 (d) ₹168
15. 15.If 5 notebooks cost ₹105, how much do 7 notebooks cost? (a) ₹735 (b) ₹147 (c) ₹168 (d) ₹107
16. 16.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 10 days (d) 8 days
17. 17.If 9 mangoes cost ₹45, how much do 11 mangoes cost? (a) ₹55 (b) ₹495 (c) ₹47 (d) ₹60
18. 18.₹377 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹290 (b) ₹116 (c) ₹29 (d) ₹261
19. 19.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹264 (b) ₹308 (c) ₹44 (d) ₹154
20. 20.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 7 days
21. 21.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 54 days (c) 5 days (d) 55 days
22. 22.If 2 mangoes cost ₹6, how much do 4 mangoes cost? (a) ₹15 (b) ₹8 (c) ₹12 (d) ₹24
23. 23.If 7 mangoes cost ₹112, how much do 2 mangoes cost? (a) ₹32 (b) ₹48 (c) ₹224 (d) ₹107
24. 24.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹100 (d) ₹140
25. 25.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 17 days (d) 34 days
26. 26.If 4 pens cost ₹96, how much do 3 pens cost? (a) ₹72 (b) ₹95 (c) ₹288 (d) ₹96
27. 27.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹56 (c) ₹16 (d) ₹96
28. 28.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 6 days
29. 29.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹56 (b) ₹48 (c) ₹64 (d) ₹16
30. 30.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹126 (b) ₹14 (c) ₹70 (d) ₹140
31. 31.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 7 days (d) 40 days
32. 32.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 19 days (d) 12 days
33. 33.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 5 days
34. 34.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 4 days (d) 15 days
35. 35.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 27 days (d) 26 days
36. 36.If 2 notebooks cost ₹44, how much do 6 notebooks cost? (a) ₹154 (b) ₹264 (c) ₹132 (d) ₹48
37. 37.If 6 notebooks cost ₹96, how much do 8 notebooks cost? (a) ₹98 (b) ₹768 (c) ₹144 (d) ₹128
38. 38.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹35 (d) ₹42
39. 39.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹54 (d) ₹9
40. 40.If 6 notebooks cost ₹90, how much do 11 notebooks cost? (a) ₹95 (b) ₹180 (c) ₹990 (d) ₹165

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