Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 379 · 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. 1.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 21 days (d) 22 days
2. 2.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 20 days (d) 14 days
3. 3.If 8 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹47 (b) ₹336 (c) ₹42 (d) ₹48
4. 4.If 4 kites cost ₹52, how much do 9 kites cost? (a) ₹468 (b) ₹57 (c) ₹117 (d) ₹130
5. 5.If 7 pens cost ₹119, how much do 10 pens cost? (a) ₹187 (b) ₹1190 (c) ₹122 (d) ₹170
6. 6.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹21 (b) ₹14 (c) ₹28 (d) ₹7
7. 7.₹350 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹175 (b) ₹245 (c) ₹35 (d) ₹105
8. 8.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 4 days (d) 3 days
9. 9.If 4 kites cost ₹80, how much do 11 kites cost? (a) ₹87 (b) ₹220 (c) ₹240 (d) ₹880
10. 10.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
11. 11.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 1 day (d) 8 days
12. 12.If 6 kites cost ₹144, how much do 5 kites cost? (a) ₹720 (b) ₹143 (c) ₹120 (d) ₹144
13. 13.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹119 (d) ₹136
14. 14.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹39 (b) ₹390 (c) ₹78 (d) ₹351
15. 15.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 11 days
16. 16.If 3 mangoes cost ₹57, how much do 7 mangoes cost? (a) ₹399 (b) ₹133 (c) ₹61 (d) ₹152
17. 17.If 8 pens cost ₹120, how much do 11 pens cost? (a) ₹1320 (b) ₹180 (c) ₹123 (d) ₹165
18. 18.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹144 (c) ₹160 (d) ₹16
19. 19.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 4 days (d) 3 days
20. 20.If 4 pens cost ₹76, how much do 8 pens cost? (a) ₹171 (b) ₹80 (c) ₹152 (d) ₹608
21. 21.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
22. 22.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 27 days (c) 10 days (d) 26 days
23. 23.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹91 (b) ₹104 (c) ₹13 (d) ₹52
24. 24.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 1 day (d) 2 days
25. 25.If 2 pens cost ₹10, how much do 6 pens cost? (a) ₹60 (b) ₹14 (c) ₹35 (d) ₹30
26. 26.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 1 day
27. 27.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 7 days
28. 28.If 4 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹47 (b) ₹120 (c) ₹440 (d) ₹110
29. 29.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹8 (c) ₹56 (d) ₹16
30. 30.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹48 (b) ₹8 (c) ₹44 (d) ₹40
31. 31.If 6 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹420 (b) ₹70 (c) ₹77 (d) ₹46
32. 32.₹341 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹310 (b) ₹279 (c) ₹62 (d) ₹31
33. 33.If 5 mangoes cost ₹110, how much do 12 mangoes cost? (a) ₹264 (b) ₹286 (c) ₹1320 (d) ₹117
34. 34.If 5 pens cost ₹45, how much do 4 pens cost? (a) ₹44 (b) ₹180 (c) ₹45 (d) ₹36
35. 35.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹42 (b) ₹56 (c) ₹14 (d) ₹49
36. 36.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹240 (c) ₹280 (d) ₹200
37. 37.₹520 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹260 (b) ₹320 (c) ₹200 (d) ₹40
38. 38.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹240 (d) ₹40
39. 39.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 12 days (d) 8 days
40. 40.If 4 mangoes cost ₹16, how much do 6 mangoes cost? (a) ₹28 (b) ₹96 (c) ₹24 (d) ₹18

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