Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 566 · 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 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 13 days (d) 7 days
2. 2.If 4 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹14 (b) ₹18 (c) ₹72 (d) ₹21
3. 3.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 4 days
4. 4.If 4 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹24 (b) ₹96 (c) ₹36 (d) ₹46
5. 5.If 6 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹74 (b) ₹96 (c) ₹108 (d) ₹576
6. 6.If 2 kites cost ₹36, how much do 7 kites cost? (a) ₹252 (b) ₹41 (c) ₹126 (d) ₹144
7. 7.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 18 days (d) 19 days
8. 8.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹45 (c) ₹63 (d) ₹9
9. 9.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 40 days (d) 39 days
10. 10.If 8 notebooks cost ₹128, how much do 12 notebooks cost? (a) ₹132 (b) ₹1536 (c) ₹208 (d) ₹192
11. 11.If 3 pens cost ₹57, how much do 5 pens cost? (a) ₹59 (b) ₹114 (c) ₹95 (d) ₹285
12. 12.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹150 (b) ₹100 (c) ₹50 (d) ₹75
13. 13.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
14. 14.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹140 (d) ₹120
15. 15.If 2 notebooks cost ₹22, how much do 4 notebooks cost? (a) ₹55 (b) ₹44 (c) ₹24 (d) ₹88
16. 16.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 18 days (d) 7 days
17. 17.If 7 pens cost ₹35, how much do 6 pens cost? (a) ₹210 (b) ₹30 (c) ₹34 (d) ₹35
18. 18.If 7 kites cost ₹175, how much do 12 kites cost? (a) ₹2100 (b) ₹325 (c) ₹180 (d) ₹300
19. 19.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹280 (c) ₹120 (d) ₹40
20. 20.If 4 mangoes cost ₹12, how much do 12 mangoes cost? (a) ₹144 (b) ₹20 (c) ₹39 (d) ₹36
21. 21.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 5 days (d) 9 days
22. 22.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹21 (c) ₹126 (d) ₹105
23. 23.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 4 days (d) 3 days
24. 24.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹61 (d) ₹60
25. 25.If 9 pens cost ₹54, how much do 10 pens cost? (a) ₹60 (b) ₹540 (c) ₹55 (d) ₹66
26. 26.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹120 (b) ₹192 (c) ₹156 (d) ₹24
27. 27.If 7 notebooks cost ₹112, how much do 3 notebooks cost? (a) ₹336 (b) ₹48 (c) ₹108 (d) ₹64
28. 28.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 21 days (c) 16 days (d) 22 days
29. 29.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
30. 30.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 9 days (d) 10 days
31. 31.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 7 days
32. 32.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 18 days (d) 4 days
33. 33.If 2 mangoes cost ₹38, how much do 6 mangoes cost? (a) ₹42 (b) ₹133 (c) ₹228 (d) ₹114
34. 34.If 2 kites cost ₹28, how much do 12 kites cost? (a) ₹336 (b) ₹38 (c) ₹168 (d) ₹182
35. 35.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹352 (c) ₹308 (d) ₹176
36. 36.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 11 days (d) 12 days
37. 37.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹37 (b) ₹333 (c) ₹297 (d) ₹296
38. 38.If 7 notebooks cost ₹42, how much do 11 notebooks cost? (a) ₹462 (b) ₹66 (c) ₹46 (d) ₹72
39. 39.If 8 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹37 (b) ₹200 (c) ₹30 (d) ₹25
40. 40.If 4 kites cost ₹100, how much do 2 kites cost? (a) ₹75 (b) ₹200 (c) ₹98 (d) ₹50

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