Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 572 · 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.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹176 (d) ₹143
2. 2.If 8 pens cost ₹144, how much do 11 pens cost? (a) ₹198 (b) ₹147 (c) ₹1584 (d) ₹216
3. 3.If 2 pens cost ₹16, how much do 6 pens cost? (a) ₹56 (b) ₹20 (c) ₹96 (d) ₹48
4. 4.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 15 days (d) 14 days
5. 5.₹138 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹69 (b) ₹138 (c) ₹115 (d) ₹23
6. 6.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹154 (b) ₹44 (c) ₹22 (d) ₹99
7. 7.If 3 notebooks cost ₹27, how much do 4 notebooks cost? (a) ₹36 (b) ₹45 (c) ₹108 (d) ₹28
8. 8.If 9 notebooks cost ₹216, how much do 10 notebooks cost? (a) ₹2160 (b) ₹264 (c) ₹240 (d) ₹217
9. 9.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹154 (d) ₹132
10. 10.If 6 pens cost ₹144, how much do 2 pens cost? (a) ₹288 (b) ₹48 (c) ₹140 (d) ₹72
11. 11.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹28 (d) ₹21
12. 12.₹517 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹94 (b) ₹47 (c) ₹423 (d) ₹470
13. 13.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹120 (d) ₹280
14. 14.₹405 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹361 (b) ₹45 (c) ₹360 (d) ₹405
15. 15.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹35 (d) ₹20
16. 16.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
17. 17.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹9 (b) ₹73 (c) ₹81 (d) ₹72
18. 18.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹9 (b) ₹7 (c) ₹18 (d) ₹12
19. 19.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
20. 20.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹48 (b) ₹192 (c) ₹240 (d) ₹144
21. 21.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 16 days (d) 5 days
22. 22.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 18 days (d) 10 days
23. 23.If 2 pens cost ₹24, how much do 8 pens cost? (a) ₹192 (b) ₹96 (c) ₹108 (d) ₹30
24. 24.If 6 mangoes cost ₹108, how much do 12 mangoes cost? (a) ₹114 (b) ₹234 (c) ₹216 (d) ₹1296
25. 25.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹14 (b) ₹70 (c) ₹42 (d) ₹98
26. 26.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 24 days (d) 8 days
27. 27.If 8 notebooks cost ₹96, how much do 2 notebooks cost? (a) ₹90 (b) ₹36 (c) ₹192 (d) ₹24
28. 28.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 12 days (d) 2 days
29. 29.₹18 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹6 (d) ₹12
30. 30.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
31. 31.If 8 mangoes cost ₹96, how much do 11 mangoes cost? (a) ₹99 (b) ₹1056 (c) ₹132 (d) ₹144
32. 32.If 9 kites cost ₹72, how much do 6 kites cost? (a) ₹69 (b) ₹48 (c) ₹56 (d) ₹432
33. 33.If 3 notebooks cost ₹42, how much do 7 notebooks cost? (a) ₹98 (b) ₹46 (c) ₹112 (d) ₹294
34. 34.If 9 mangoes cost ₹90, how much do 8 mangoes cost? (a) ₹90 (b) ₹89 (c) ₹720 (d) ₹80
35. 35.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹272 (b) ₹153 (c) ₹306 (d) ₹34
36. 36.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹126 (b) ₹21 (c) ₹105 (d) ₹147
37. 37.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 13 days (d) 21 days
38. 38.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 4 days
39. 39.If 7 kites cost ₹126, how much do 5 kites cost? (a) ₹108 (b) ₹90 (c) ₹124 (d) ₹630
40. 40.₹320 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹160 (c) ₹40 (d) ₹200

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