Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 206 · 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 ₹22, how much do 4 mangoes cost? (a) ₹24 (b) ₹88 (c) ₹44 (d) ₹55
2. 2.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹49 (c) ₹7 (d) ₹35
3. 3.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹65 (d) ₹90
4. 4.If 4 kites cost ₹72, how much do 9 kites cost? (a) ₹180 (b) ₹648 (c) ₹77 (d) ₹162
5. 5.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 4 days (d) 2 days
6. 6.If 9 mangoes cost ₹216, how much do 8 mangoes cost? (a) ₹215 (b) ₹192 (c) ₹1728 (d) ₹216
7. 7.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 12 days (c) 7 days (d) 16 days
8. 8.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
9. 9.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 7 days
10. 10.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹360 (b) ₹315 (c) ₹45 (d) ₹90
11. 11.If 5 pens cost ₹35, how much do 10 pens cost? (a) ₹40 (b) ₹350 (c) ₹70 (d) ₹77
12. 12.If 5 kites cost ₹15, how much do 6 kites cost? (a) ₹16 (b) ₹21 (c) ₹90 (d) ₹18
13. 13.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹42 (c) ₹12 (d) ₹48
14. 14.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 27 days (d) 28 days
15. 15.If 8 mangoes cost ₹168, how much do 5 mangoes cost? (a) ₹105 (b) ₹126 (c) ₹165 (d) ₹840
16. 16.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹99 (d) ₹198
17. 17.If 8 kites cost ₹32, how much do 9 kites cost? (a) ₹36 (b) ₹288 (c) ₹33 (d) ₹40
18. 18.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹246 (b) ₹287 (c) ₹205 (d) ₹41
19. 19.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹185 (d) ₹333
20. 20.If 7 kites cost ₹161, how much do 8 kites cost? (a) ₹162 (b) ₹184 (c) ₹207 (d) ₹1288
21. 21.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹42 (b) ₹189 (c) ₹336 (d) ₹378
22. 22.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 11 days (d) 16 days
23. 23.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹43 (b) ₹430 (c) ₹387 (d) ₹86
24. 24.If 3 pens cost ₹54, how much do 12 pens cost? (a) ₹234 (b) ₹648 (c) ₹63 (d) ₹216
25. 25.If 7 pens cost ₹154, how much do 11 pens cost? (a) ₹264 (b) ₹1694 (c) ₹158 (d) ₹242
26. 26.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 8 days (d) 10 days
27. 27.If 9 notebooks cost ₹207, how much do 7 notebooks cost? (a) ₹161 (b) ₹1449 (c) ₹205 (d) ₹184
28. 28.If 2 pens cost ₹26, how much do 4 pens cost? (a) ₹52 (b) ₹65 (c) ₹28 (d) ₹104
29. 29.If 2 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹252 (b) ₹504 (c) ₹52 (d) ₹273
30. 30.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹176 (b) ₹32 (c) ₹160 (d) ₹192
31. 31.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 5 days (d) 4 days
32. 32.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 6 days
33. 33.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹10 (c) ₹45 (d) ₹80
34. 34.If 8 kites cost ₹152, how much do 2 kites cost? (a) ₹146 (b) ₹38 (c) ₹57 (d) ₹304
35. 35.If 5 mangoes cost ₹110, how much do 3 mangoes cost? (a) ₹66 (b) ₹108 (c) ₹330 (d) ₹88
36. 36.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹88 (b) ₹198 (c) ₹44 (d) ₹308
37. 37.If 5 pens cost ₹35, how much do 7 pens cost? (a) ₹245 (b) ₹37 (c) ₹56 (d) ₹49
38. 38.If 8 pens cost ₹96, how much do 2 pens cost? (a) ₹36 (b) ₹24 (c) ₹90 (d) ₹192
39. 39.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 10 days (d) 2 days
40. 40.If 5 notebooks cost ₹15, how much do 11 notebooks cost? (a) ₹36 (b) ₹33 (c) ₹21 (d) ₹165

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