Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 270 · 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.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹23 (b) ₹33 (c) ₹22 (d) ₹11
2. 2.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 13 days (d) 9 days
3. 3.If 4 mangoes cost ₹80, how much do 3 mangoes cost? (a) ₹80 (b) ₹60 (c) ₹79 (d) ₹240
4. 4.If 8 notebooks cost ₹112, how much do 2 notebooks cost? (a) ₹224 (b) ₹106 (c) ₹42 (d) ₹28
5. 5.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹72 (b) ₹216 (c) ₹55 (d) ₹90
6. 6.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 7 days (d) 6 days
7. 7.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹145 (b) ₹87 (c) ₹29 (d) ₹203
8. 8.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 8 days
9. 9.₹336 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹168 (b) ₹96 (c) ₹48 (d) ₹240
10. 10.If 8 pens cost ₹120, how much do 2 pens cost? (a) ₹114 (b) ₹30 (c) ₹240 (d) ₹45
11. 11.₹88 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹22 (b) ₹44 (c) ₹88 (d) ₹66
12. 12.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 13 days
13. 13.If 4 kites cost ₹68, how much do 6 kites cost? (a) ₹70 (b) ₹408 (c) ₹102 (d) ₹119
14. 14.If 2 notebooks cost ₹28, how much do 4 notebooks cost? (a) ₹112 (b) ₹30 (c) ₹70 (d) ₹56
15. 15.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 10 days
16. 16.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 13 days (d) 27 days
17. 17.If 5 notebooks cost ₹115, how much do 2 notebooks cost? (a) ₹112 (b) ₹46 (c) ₹69 (d) ₹230
18. 18.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹168 (b) ₹24 (c) ₹22 (d) ₹27
19. 19.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹93 (b) ₹155 (c) ₹217 (d) ₹31
20. 20.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
21. 21.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 15 days (d) 14 days
22. 22.If 8 notebooks cost ₹168, how much do 12 notebooks cost? (a) ₹2016 (b) ₹172 (c) ₹252 (d) ₹273
23. 23.9 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
24. 24.If 8 notebooks cost ₹184, how much do 4 notebooks cost? (a) ₹180 (b) ₹92 (c) ₹115 (d) ₹736
25. 25.If 5 kites cost ₹90, how much do 2 kites cost? (a) ₹36 (b) ₹54 (c) ₹180 (d) ₹87
26. 26.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 5 days (d) 7 days
27. 27.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹98 (b) ₹70 (c) ₹14 (d) ₹84
28. 28.If 7 mangoes cost ₹35, how much do 8 mangoes cost? (a) ₹36 (b) ₹280 (c) ₹45 (d) ₹40
29. 29.If 8 kites cost ₹32, how much do 12 kites cost? (a) ₹52 (b) ₹36 (c) ₹48 (d) ₹384
30. 30.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹30 (d) ₹50
31. 31.If 4 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹160 (b) ₹45 (c) ₹24 (d) ₹40
32. 32.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹310 (d) ₹279
33. 33.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 20 days (d) 5 days
34. 34.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 14 days (d) 8 days
35. 35.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹80 (d) ₹96
36. 36.If 9 kites cost ₹153, how much do 2 kites cost? (a) ₹34 (b) ₹306 (c) ₹51 (d) ₹146
37. 37.If 6 pens cost ₹66, how much do 7 pens cost? (a) ₹67 (b) ₹77 (c) ₹462 (d) ₹88
38. 38.If 5 pens cost ₹65, how much do 6 pens cost? (a) ₹66 (b) ₹78 (c) ₹390 (d) ₹91
39. 39.If 6 mangoes cost ₹132, how much do 8 mangoes cost? (a) ₹134 (b) ₹198 (c) ₹176 (d) ₹1056
40. 40.₹420 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹378 (b) ₹210 (c) ₹420 (d) ₹42

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