Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 114 · 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 4 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹99 (b) ₹360 (c) ₹42 (d) ₹90
2. 2.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 11 days
3. 3.If 2 mangoes cost ₹32, how much do 5 mangoes cost? (a) ₹80 (b) ₹35 (c) ₹160 (d) ₹96
4. 4.If 2 kites cost ₹10, how much do 9 kites cost? (a) ₹90 (b) ₹17 (c) ₹50 (d) ₹45
5. 5.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹135 (d) ₹91
6. 6.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 49 days (d) 4 days
7. 7.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹225 (b) ₹201 (c) ₹25 (d) ₹200
8. 8.If 2 mangoes cost ₹26, how much do 7 mangoes cost? (a) ₹182 (b) ₹104 (c) ₹31 (d) ₹91
9. 9.If 6 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹144 (b) ₹30 (c) ₹24 (d) ₹34
10. 10.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹90 (d) ₹81
11. 11.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 18 days (d) 7 days
12. 12.If 3 mangoes cost ₹39, how much do 8 mangoes cost? (a) ₹312 (b) ₹44 (c) ₹104 (d) ₹117
13. 13.If 3 kites cost ₹60, how much do 7 kites cost? (a) ₹140 (b) ₹420 (c) ₹64 (d) ₹160
14. 14.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 6 days (d) 7 days
15. 15.If 5 kites cost ₹25, how much do 8 kites cost? (a) ₹45 (b) ₹40 (c) ₹200 (d) ₹28
16. 16.If 5 pens cost ₹80, how much do 9 pens cost? (a) ₹144 (b) ₹160 (c) ₹720 (d) ₹84
17. 17.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 11 days (d) 5 days
18. 18.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 4 days (d) 5 days
19. 19.If 7 kites cost ₹168, how much do 11 kites cost? (a) ₹264 (b) ₹172 (c) ₹288 (d) ₹1848
20. 20.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 19 days
21. 21.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹70 (b) ₹63 (c) ₹14 (d) ₹56
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 28 days
23. 23.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹168 (d) ₹21
24. 24.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹35 (c) ₹49 (d) ₹7
25. 25.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹20 (b) ₹200 (c) ₹100 (d) ₹180
26. 26.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹112 (b) ₹64 (c) ₹16 (d) ₹128
27. 27.If 9 kites cost ₹81, how much do 12 kites cost? (a) ₹84 (b) ₹972 (c) ₹117 (d) ₹108
28. 28.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹266 (b) ₹38 (c) ₹190 (d) ₹342
29. 29.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹370 (b) ₹37 (c) ₹333 (d) ₹148
30. 30.If 3 notebooks cost ₹15, how much do 2 notebooks cost? (a) ₹15 (b) ₹30 (c) ₹14 (d) ₹10
31. 31.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 7 days (d) 2 days
32. 32.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 13 days (d) 12 days
33. 33.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹85 (d) ₹68
34. 34.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 18 days (d) 19 days
35. 35.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 7 days (d) 8 days
36. 36.₹144 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹72 (b) ₹96 (c) ₹144 (d) ₹48
37. 37.If 3 pens cost ₹60, how much do 6 pens cost? (a) ₹63 (b) ₹120 (c) ₹360 (d) ₹140
38. 38.3 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) 4 days (d) 3 days
39. 39.If 8 kites cost ₹24, how much do 3 kites cost? (a) ₹72 (b) ₹12 (c) ₹9 (d) ₹19
40. 40.If 2 mangoes cost ₹38, how much do 3 mangoes cost? (a) ₹39 (b) ₹76 (c) ₹114 (d) ₹57

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