Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 538 · 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. 1.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 7 days
2. 2.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹220
3. 3.₹364 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹28 (b) ₹182 (c) ₹112 (d) ₹252
4. 4.If 8 mangoes cost ₹96, how much do 4 mangoes cost? (a) ₹92 (b) ₹48 (c) ₹60 (d) ₹384
5. 5.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days
6. 6.If 3 pens cost ₹27, how much do 4 pens cost? (a) ₹28 (b) ₹45 (c) ₹36 (d) ₹108
7. 7.₹272 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹34 (b) ₹136 (c) ₹170 (d) ₹102
8. 8.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 36 days (d) 35 days
9. 9.₹152 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹76 (b) ₹57 (c) ₹95 (d) ₹19
10. 10.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 11 days (d) 16 days
11. 11.If 2 mangoes cost ₹26, how much do 8 mangoes cost? (a) ₹208 (b) ₹32 (c) ₹117 (d) ₹104
12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 5 days
13. 13.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 4 days (d) 9 days
14. 14.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 10 days (d) 18 days
15. 15.₹328 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹164 (b) ₹287 (c) ₹41 (d) ₹328
16. 16.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 10 days (c) 2 days (d) 18 days
17. 17.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 18 days (d) 10 days
18. 18.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 14 days (d) 19 days
19. 19.If 7 pens cost ₹133, how much do 9 pens cost? (a) ₹171 (b) ₹1197 (c) ₹135 (d) ₹190
20. 20.If 8 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹21 (b) ₹120 (c) ₹15 (d) ₹18
21. 21.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 2 days (d) 8 days
22. 22.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹96 (b) ₹49 (c) ₹72 (d) ₹144
23. 23.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 1 day
24. 24.If 5 kites cost ₹25, how much do 11 kites cost? (a) ₹55 (b) ₹31 (c) ₹275 (d) ₹60
25. 25.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹120 (b) ₹110 (c) ₹100 (d) ₹20
26. 26.If 4 mangoes cost ₹64, how much do 9 mangoes cost? (a) ₹160 (b) ₹69 (c) ₹144 (d) ₹576
27. 27.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 17 days (c) 9 days (d) 39 days
28. 28.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 1 day
29. 29.If 8 notebooks cost ₹152, how much do 9 notebooks cost? (a) ₹171 (b) ₹1368 (c) ₹190 (d) ₹153
30. 30.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹54 (b) ₹90 (c) ₹126 (d) ₹18
31. 31.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹238 (b) ₹170 (c) ₹204 (d) ₹34
32. 32.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹16 (b) ₹20 (c) ₹25 (d) ₹60
33. 33.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹207 (b) ₹23 (c) ₹115 (d) ₹230
34. 34.If 3 kites cost ₹48, how much do 2 kites cost? (a) ₹47 (b) ₹96 (c) ₹48 (d) ₹32
35. 35.If 6 pens cost ₹18, how much do 2 pens cost? (a) ₹14 (b) ₹9 (c) ₹36 (d) ₹6
36. 36.If 7 mangoes cost ₹105, how much do 8 mangoes cost? (a) ₹840 (b) ₹120 (c) ₹106 (d) ₹135
37. 37.If 8 notebooks cost ₹144, how much do 12 notebooks cost? (a) ₹234 (b) ₹1728 (c) ₹148 (d) ₹216
38. 38.If 8 kites cost ₹168, how much do 9 kites cost? (a) ₹1512 (b) ₹169 (c) ₹189 (d) ₹210
39. 39.If 9 pens cost ₹81, how much do 6 pens cost? (a) ₹486 (b) ₹54 (c) ₹63 (d) ₹78
40. 40.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 14 days

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