Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 515 · 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 6 kites cost ₹138, how much do 4 kites cost? (a) ₹92 (b) ₹136 (c) ₹552 (d) ₹115
2. 2.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹144 (d) ₹180
3. 3.If 9 kites cost ₹45, how much do 5 kites cost? (a) ₹25 (b) ₹225 (c) ₹41 (d) ₹30
4. 4.₹300 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹30 (b) ₹300 (c) ₹150 (d) ₹270
5. 5.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 21 days (c) 22 days (d) 11 days
6. 6.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹282 (d) ₹235
7. 7.₹240 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹240 (b) ₹120 (c) ₹210 (d) ₹30
8. 8.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 11 days (d) 18 days
9. 9.If 9 pens cost ₹144, how much do 3 pens cost? (a) ₹138 (b) ₹48 (c) ₹432 (d) ₹64
10. 10.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 9 days (d) 13 days
11. 11.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹266 (d) ₹171
12. 12.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹171 (b) ₹19 (c) ₹152 (d) ₹57
13. 13.If 6 pens cost ₹72, how much do 9 pens cost? (a) ₹75 (b) ₹648 (c) ₹120 (d) ₹108
14. 14.₹341 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹279 (d) ₹93
15. 15.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 4 days (d) 25 days
16. 16.If 8 notebooks cost ₹32, how much do 6 notebooks cost? (a) ₹30 (b) ₹192 (c) ₹28 (d) ₹24
17. 17.If 7 kites cost ₹112, how much do 12 kites cost? (a) ₹192 (b) ₹1344 (c) ₹117 (d) ₹208
18. 18.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 3 days
19. 19.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 13 days (d) 27 days
20. 20.If 2 notebooks cost ₹22, how much do 12 notebooks cost? (a) ₹143 (b) ₹264 (c) ₹132 (d) ₹32
21. 21.If 2 kites cost ₹42, how much do 11 kites cost? (a) ₹462 (b) ₹252 (c) ₹231 (d) ₹51
22. 22.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 9 days
23. 23.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹234 (b) ₹180 (c) ₹36 (d) ₹288
24. 24.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 21 days (d) 5 days
25. 25.If 2 pens cost ₹12, how much do 4 pens cost? (a) ₹48 (b) ₹30 (c) ₹14 (d) ₹24
26. 26.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 36 days (c) 11 days (d) 35 days
27. 27.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹49 (b) ₹35 (c) ₹63 (d) ₹7
28. 28.If 6 kites cost ₹132, how much do 8 kites cost? (a) ₹134 (b) ₹198 (c) ₹1056 (d) ₹176
29. 29.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹117 (b) ₹39 (c) ₹79 (d) ₹78
30. 30.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
31. 31.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹56 (d) ₹24
32. 32.If 6 mangoes cost ₹18, how much do 3 mangoes cost? (a) ₹9 (b) ₹12 (c) ₹54 (d) ₹15
33. 33.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹187 (b) ₹204 (c) ₹170 (d) ₹34
34. 34.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 11 days (d) 15 days
35. 35.If 5 notebooks cost ₹15, how much do 10 notebooks cost? (a) ₹150 (b) ₹30 (c) ₹33 (d) ₹20
36. 36.If 3 pens cost ₹63, how much do 12 pens cost? (a) ₹252 (b) ₹273 (c) ₹72 (d) ₹756
37. 37.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹147 (d) ₹99
38. 38.If 3 pens cost ₹54, how much do 12 pens cost? (a) ₹216 (b) ₹648 (c) ₹63 (d) ₹234
39. 39.If 3 kites cost ₹72, how much do 4 kites cost? (a) ₹96 (b) ₹120 (c) ₹73 (d) ₹288
40. 40.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹72 (c) ₹9 (d) ₹27

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