Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 216 · 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 2 kites cost? (a) ₹134 (b) ₹276 (c) ₹69 (d) ₹46
2. 2.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 18 days (d) 15 days
3. 3.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹243 (b) ₹135 (c) ₹216 (d) ₹27
4. 4.If 8 pens cost ₹64, how much do 12 pens cost? (a) ₹96 (b) ₹768 (c) ₹104 (d) ₹68
5. 5.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹38 (b) ₹39 (c) ₹57 (d) ₹19
6. 6.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹228 (b) ₹190 (c) ₹114 (d) ₹38
7. 7.₹180 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹180 (c) ₹162 (d) ₹18
8. 8.₹72 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹63 (d) ₹72
9. 9.3 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) 17 days (d) 13 days
10. 10.If 5 kites cost ₹90, how much do 9 kites cost? (a) ₹180 (b) ₹94 (c) ₹162 (d) ₹810
11. 11.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 4 days (d) 3 days
12. 12.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 16 days (c) 12 days (d) 22 days
13. 13.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹15 (c) ₹20 (d) ₹30
14. 14.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹161 (b) ₹23 (c) ₹184 (d) ₹92
15. 15.If 9 kites cost ₹216, how much do 3 kites cost? (a) ₹96 (b) ₹72 (c) ₹648 (d) ₹210
16. 16.If 6 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹72 (b) ₹56 (c) ₹81 (d) ₹432
17. 17.7 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
18. 18.If 2 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹200 (b) ₹360 (c) ₹180 (d) ₹47
19. 19.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 39 days (d) 19 days
20. 20.If 5 pens cost ₹40, how much do 10 pens cost? (a) ₹45 (b) ₹80 (c) ₹400 (d) ₹88
21. 21.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹33 (c) ₹55 (d) ₹11
22. 22.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 14 days (d) 11 days
23. 23.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹288 (b) ₹176 (c) ₹64 (d) ₹32
24. 24.If 9 kites cost ₹108, how much do 11 kites cost? (a) ₹110 (b) ₹132 (c) ₹1188 (d) ₹144
25. 25.If 5 kites cost ₹100, how much do 4 kites cost? (a) ₹99 (b) ₹80 (c) ₹100 (d) ₹400
26. 26.If 2 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹50 (b) ₹80 (c) ₹40 (d) ₹22
27. 27.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 11 days
28. 28.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 3 days (d) 4 days
29. 29.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹114 (b) ₹38 (c) ₹95 (d) ₹76
30. 30.If 7 pens cost ₹119, how much do 8 pens cost? (a) ₹952 (b) ₹153 (c) ₹120 (d) ₹136
31. 31.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹64 (b) ₹224 (c) ₹32 (d) ₹144
32. 32.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 3 days (c) 13 days (d) 28 days
33. 33.If 3 kites cost ₹75, how much do 10 kites cost? (a) ₹275 (b) ₹82 (c) ₹750 (d) ₹250
34. 34.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 10 days (d) 9 days
35. 35.If 4 notebooks cost ₹92, how much do 10 notebooks cost? (a) ₹230 (b) ₹920 (c) ₹98 (d) ₹253
36. 36.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 3 days (c) 11 days (d) 22 days
37. 37.If 3 notebooks cost ₹24, how much do 6 notebooks cost? (a) ₹48 (b) ₹27 (c) ₹144 (d) ₹56
38. 38.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹153 (b) ₹85 (c) ₹119 (d) ₹17
39. 39.₹222 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹111 (b) ₹185 (c) ₹37 (d) ₹222
40. 40.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹207 (d) ₹23

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