Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 100 · 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 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹50 (b) ₹120 (c) ₹96 (d) ₹192
2. 2.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹27 (d) ₹36
3. 3.If 4 pens cost ₹100, how much do 5 pens cost? (a) ₹500 (b) ₹150 (c) ₹101 (d) ₹125
4. 4.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 17 days (d) 13 days
5. 5.If 4 mangoes cost ₹68, how much do 10 mangoes cost? (a) ₹187 (b) ₹74 (c) ₹680 (d) ₹170
6. 6.₹286 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹78 (b) ₹208 (c) ₹143 (d) ₹26
7. 7.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 6 days (d) 16 days
8. 8.If 9 notebooks cost ₹189, how much do 11 notebooks cost? (a) ₹252 (b) ₹231 (c) ₹2079 (d) ₹191
9. 9.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹60 (d) ₹96
10. 10.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹36 (d) ₹30
11. 11.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 27 days (d) 19 days
12. 12.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹333 (b) ₹296 (c) ₹37 (d) ₹111
13. 13.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹54 (b) ₹19 (c) ₹27 (d) ₹36
14. 14.₹100 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹10 (c) ₹50 (d) ₹100
15. 15.If 4 pens cost ₹32, how much do 7 pens cost? (a) ₹64 (b) ₹35 (c) ₹56 (d) ₹224
16. 16.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 16 days (d) 12 days
17. 17.If 9 kites cost ₹225, how much do 10 kites cost? (a) ₹226 (b) ₹2250 (c) ₹275 (d) ₹250
18. 18.If 3 pens cost ₹21, how much do 7 pens cost? (a) ₹147 (b) ₹25 (c) ₹56 (d) ₹49
19. 19.If 5 kites cost ₹55, how much do 9 kites cost? (a) ₹110 (b) ₹99 (c) ₹59 (d) ₹495
20. 20.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹39 (d) ₹27
21. 21.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹171 (b) ₹95 (c) ₹190 (d) ₹19
22. 22.If 5 kites cost ₹125, how much do 10 kites cost? (a) ₹250 (b) ₹130 (c) ₹275 (d) ₹1250
23. 23.If 9 kites cost ₹189, how much do 12 kites cost? (a) ₹2268 (b) ₹252 (c) ₹273 (d) ₹192
24. 24.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹75 (c) ₹15 (d) ₹60
25. 25.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹56 (d) ₹24
26. 26.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹35 (d) ₹42
27. 27.If 8 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹432 (b) ₹60 (c) ₹54 (d) ₹49
28. 28.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 13 days
29. 29.If 6 pens cost ₹102, how much do 4 pens cost? (a) ₹68 (b) ₹100 (c) ₹85 (d) ₹408
30. 30.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹270 (b) ₹315 (c) ₹45 (d) ₹225
31. 31.If 2 kites cost ₹6, how much do 5 kites cost? (a) ₹15 (b) ₹30 (c) ₹18 (d) ₹9
32. 32.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹48 (c) ₹240 (d) ₹336
33. 33.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹66 (b) ₹110 (c) ₹88 (d) ₹22
34. 34.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹28 (d) ₹56
35. 35.If 2 notebooks cost ₹8, how much do 12 notebooks cost? (a) ₹18 (b) ₹48 (c) ₹52 (d) ₹96
36. 36.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 9 days (d) 3 days
37. 37.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹116 (b) ₹203 (c) ₹29 (d) ₹232
38. 38.If 5 pens cost ₹15, how much do 4 pens cost? (a) ₹15 (b) ₹14 (c) ₹12 (d) ₹60
39. 39.If 6 mangoes cost ₹144, how much do 4 mangoes cost? (a) ₹142 (b) ₹120 (c) ₹576 (d) ₹96
40. 40.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 5 days (d) 9 days

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