Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 902 · 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.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹171 (d) ₹19
2. 2.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
3. 3.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹16 (c) ₹24 (d) ₹20
4. 4.If 3 kites cost ₹30, how much do 9 kites cost? (a) ₹270 (b) ₹36 (c) ₹90 (d) ₹100
5. 5.If 4 mangoes cost ₹32, how much do 10 mangoes cost? (a) ₹320 (b) ₹88 (c) ₹38 (d) ₹80
6. 6.If 7 pens cost ₹56, how much do 6 pens cost? (a) ₹336 (b) ₹48 (c) ₹55 (d) ₹56
7. 7.If 3 notebooks cost ₹30, how much do 6 notebooks cost? (a) ₹180 (b) ₹33 (c) ₹70 (d) ₹60
8. 8.If 2 mangoes cost ₹48, how much do 11 mangoes cost? (a) ₹288 (b) ₹57 (c) ₹264 (d) ₹528
9. 9.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 17 days (c) 30 days (d) 13 days
10. 10.If 4 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹57 (b) ₹70 (c) ₹280 (d) ₹84
11. 11.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 9 days (d) 10 days
12. 12.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 6 days (d) 5 days
13. 13.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹22 (b) ₹154 (c) ₹176 (d) ₹88
14. 14.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 5 days (d) 3 days
15. 15.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 6 days
16. 16.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 36 days (d) 20 days
17. 17.3 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
18. 18.If 8 mangoes cost ₹128, how much do 10 mangoes cost? (a) ₹1280 (b) ₹176 (c) ₹160 (d) ₹130
19. 19.If 4 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹120 (b) ₹22 (c) ₹30 (d) ₹35
20. 20.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹67 (b) ₹33 (c) ₹66 (d) ₹99
21. 21.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹343 (b) ₹245 (c) ₹294 (d) ₹49
22. 22.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹242 (d) ₹264
23. 23.If 7 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹24 (b) ₹28 (c) ₹168 (d) ₹27
24. 24.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 7 days (d) 28 days
25. 25.If 9 kites cost ₹108, how much do 11 kites cost? (a) ₹110 (b) ₹1188 (c) ₹132 (d) ₹144
26. 26.If 7 pens cost ₹28, how much do 9 pens cost? (a) ₹252 (b) ₹36 (c) ₹40 (d) ₹30
27. 27.If 9 pens cost ₹171, how much do 2 pens cost? (a) ₹38 (b) ₹57 (c) ₹164 (d) ₹342
28. 28.If 9 notebooks cost ₹81, how much do 5 notebooks cost? (a) ₹77 (b) ₹54 (c) ₹405 (d) ₹45
29. 29.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 15 days (d) 13 days
30. 30.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 8 days (d) 12 days
31. 31.If 7 pens cost ₹49, how much do 5 pens cost? (a) ₹47 (b) ₹245 (c) ₹35 (d) ₹42
32. 32.7 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
33. 33.If 9 notebooks cost ₹108, how much do 3 notebooks cost? (a) ₹102 (b) ₹48 (c) ₹324 (d) ₹36
34. 34.If 6 notebooks cost ₹138, how much do 4 notebooks cost? (a) ₹136 (b) ₹115 (c) ₹552 (d) ₹92
35. 35.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹9 (b) ₹27 (c) ₹36 (d) ₹18
36. 36.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹55 (b) ₹132 (c) ₹34 (d) ₹44
37. 37.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹39 (b) ₹234 (c) ₹273 (d) ₹195
38. 38.If 2 notebooks cost ₹10, how much do 6 notebooks cost? (a) ₹60 (b) ₹35 (c) ₹14 (d) ₹30
39. 39.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹84 (b) ₹24 (c) ₹54 (d) ₹12
40. 40.If 4 mangoes cost ₹64, how much do 9 mangoes cost? (a) ₹576 (b) ₹160 (c) ₹144 (d) ₹69

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