Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 167 · 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. 1.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 2 days (d) 3 days
2. 2.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹308 (b) ₹176 (c) ₹352 (d) ₹44
3. 3.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹88 (b) ₹132 (c) ₹110 (d) ₹44
4. 4.If 5 pens cost ₹25, how much do 4 pens cost? (a) ₹20 (b) ₹100 (c) ₹24 (d) ₹25
5. 5.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 19 days (d) 6 days
6. 6.If 7 pens cost ₹28, how much do 3 pens cost? (a) ₹12 (b) ₹24 (c) ₹84 (d) ₹16
7. 7.If 7 mangoes cost ₹28, how much do 11 mangoes cost? (a) ₹308 (b) ₹48 (c) ₹32 (d) ₹44
8. 8.If 4 pens cost ₹76, how much do 9 pens cost? (a) ₹171 (b) ₹684 (c) ₹81 (d) ₹190
9. 9.If 2 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹288 (b) ₹144 (c) ₹160 (d) ₹39
10. 10.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 23 days (b) 8 days (c) 14 days (d) 22 days
11. 11.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹108 (d) ₹162
12. 12.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹99 (b) ₹165 (c) ₹198 (d) ₹33
13. 13.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 15 days (d) 6 days
14. 14.If 2 mangoes cost ₹14, how much do 9 mangoes cost? (a) ₹21 (b) ₹70 (c) ₹63 (d) ₹126
15. 15.If 4 kites cost ₹20, how much do 11 kites cost? (a) ₹60 (b) ₹220 (c) ₹55 (d) ₹27
16. 16.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹88 (b) ₹77 (c) ₹66 (d) ₹22
17. 17.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 1 day
18. 18.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 3 days (c) 4 days (d) 48 days
19. 19.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹235 (b) ₹329 (c) ₹47 (d) ₹282
20. 20.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹92 (b) ₹46 (c) ₹184 (d) ₹138
21. 21.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 40 days (c) 39 days (d) 9 days
22. 22.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 10 days (d) 11 days
23. 23.If 3 kites cost ₹63, how much do 2 kites cost? (a) ₹63 (b) ₹62 (c) ₹42 (d) ₹126
24. 24.If 6 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹66 (b) ₹60 (c) ₹40 (d) ₹360
25. 25.If 6 mangoes cost ₹144, how much do 11 mangoes cost? (a) ₹1584 (b) ₹288 (c) ₹264 (d) ₹149
26. 26.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 27 days (c) 10 days (d) 26 days
27. 27.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 5 days (d) 9 days
28. 28.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 11 days (d) 25 days
29. 29.If 6 mangoes cost ₹18, how much do 2 mangoes cost? (a) ₹14 (b) ₹9 (c) ₹6 (d) ₹36
30. 30.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹245 (b) ₹343 (c) ₹294 (d) ₹49
31. 31.₹504 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹294 (d) ₹252
32. 32.If 3 pens cost ₹48, how much do 4 pens cost? (a) ₹64 (b) ₹49 (c) ₹192 (d) ₹80
33. 33.If 6 pens cost ₹36, how much do 3 pens cost? (a) ₹33 (b) ₹18 (c) ₹108 (d) ₹24
34. 34.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 37 days (c) 36 days (d) 15 days
35. 35.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
36. 36.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 22 days (d) 17 days
37. 37.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
38. 38.If 4 kites cost ₹100, how much do 12 kites cost? (a) ₹1200 (b) ₹108 (c) ₹300 (d) ₹325
39. 39.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 6 days (d) 8 days
40. 40.If 7 pens cost ₹49, how much do 4 pens cost? (a) ₹35 (b) ₹28 (c) ₹196 (d) ₹46

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