Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 301 · 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 3 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹56 (b) ₹43 (c) ₹70 (d) ₹168
2. 2.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 1 day (d) 10 days
3. 3.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹77 (d) ₹88
4. 4.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 12 days (d) 6 days
5. 5.If 8 notebooks cost ₹128, how much do 3 notebooks cost? (a) ₹384 (b) ₹123 (c) ₹64 (d) ₹48
6. 6.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 25 days (c) 24 days (d) 2 days
7. 7.If 7 notebooks cost ₹161, how much do 3 notebooks cost? (a) ₹483 (b) ₹92 (c) ₹157 (d) ₹69
8. 8.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹75 (d) ₹15
9. 9.If 2 mangoes cost ₹22, how much do 11 mangoes cost? (a) ₹242 (b) ₹132 (c) ₹121 (d) ₹31
10. 10.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹120 (b) ₹30 (c) ₹165 (d) ₹210
11. 11.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 33 days (d) 32 days
12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days
13. 13.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 13 days (d) 21 days
14. 14.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹119 (c) ₹17 (d) ₹85
15. 15.₹481 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹333 (b) ₹148 (c) ₹37 (d) ₹370
16. 16.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹172 (b) ₹344 (c) ₹301 (d) ₹43
17. 17.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹15 (d) ₹45
18. 18.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 7 days (d) 19 days
19. 19.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹88 (b) ₹198 (c) ₹143 (d) ₹22
20. 20.If 2 pens cost ₹20, how much do 11 pens cost? (a) ₹220 (b) ₹110 (c) ₹29 (d) ₹120
21. 21.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 8 days (d) 2 days
22. 22.If 9 mangoes cost ₹27, how much do 7 mangoes cost? (a) ₹24 (b) ₹189 (c) ₹21 (d) ₹25
23. 23.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 10 days (d) 8 days
24. 24.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 6 days (d) 7 days
25. 25.₹144 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹72 (c) ₹144 (d) ₹96
26. 26.If 6 kites cost ₹150, how much do 7 kites cost? (a) ₹175 (b) ₹200 (c) ₹1050 (d) ₹151
27. 27.If 6 pens cost ₹102, how much do 12 pens cost? (a) ₹221 (b) ₹1224 (c) ₹108 (d) ₹204
28. 28.If 8 kites cost ₹176, how much do 5 kites cost? (a) ₹110 (b) ₹173 (c) ₹880 (d) ₹132
29. 29.If 3 pens cost ₹9, how much do 2 pens cost? (a) ₹8 (b) ₹18 (c) ₹6 (d) ₹9
30. 30.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 2 days
31. 31.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹390 (d) ₹78
32. 32.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 30 days (c) 16 days (d) 31 days
33. 33.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 32 days (d) 14 days
34. 34.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹138 (b) ₹276 (c) ₹230 (d) ₹46
35. 35.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹40 (b) ₹56 (c) ₹72 (d) ₹8
36. 36.If 3 pens cost ₹72, how much do 2 pens cost? (a) ₹71 (b) ₹48 (c) ₹144 (d) ₹72
37. 37.If 7 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹420 (b) ₹82 (c) ₹72 (d) ₹60
38. 38.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 7 days (d) 8 days
39. 39.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹78 (d) ₹182
40. 40.If 5 kites cost ₹40, how much do 4 kites cost? (a) ₹39 (b) ₹32 (c) ₹40 (d) ₹160

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