Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 226 · 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 2 pens cost ₹22, how much do 7 pens cost? (a) ₹88 (b) ₹154 (c) ₹27 (d) ₹77
2. 2.If 2 mangoes cost ₹10, how much do 7 mangoes cost? (a) ₹15 (b) ₹40 (c) ₹35 (d) ₹70
3. 3.If 2 mangoes cost ₹38, how much do 6 mangoes cost? (a) ₹42 (b) ₹114 (c) ₹133 (d) ₹228
4. 4.If 2 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹70 (b) ₹60 (c) ₹24 (d) ₹120
5. 5.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹38 (c) ₹57 (d) ₹19
6. 6.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 1 day (d) 7 days
7. 7.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹176 (c) ₹154 (d) ₹132
8. 8.If 2 mangoes cost ₹22, how much do 4 mangoes cost? (a) ₹44 (b) ₹88 (c) ₹55 (d) ₹24
9. 9.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 6 days (d) 4 days
10. 10.₹423 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹282 (b) ₹188 (c) ₹47 (d) ₹235
11. 11.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹248 (d) ₹124
12. 12.If 4 kites cost ₹40, how much do 9 kites cost? (a) ₹100 (b) ₹360 (c) ₹90 (d) ₹45
13. 13.If 8 pens cost ₹152, how much do 4 pens cost? (a) ₹608 (b) ₹148 (c) ₹76 (d) ₹95
14. 14.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 21 days (c) 22 days (d) 16 days
15. 15.₹252 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹224 (c) ₹28 (d) ₹252
16. 16.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹15 (c) ₹6 (d) ₹24
17. 17.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 8 days (c) 42 days (d) 20 days
18. 18.If 3 kites cost ₹63, how much do 10 kites cost? (a) ₹210 (b) ₹630 (c) ₹70 (d) ₹231
19. 19.If 8 kites cost ₹200, how much do 2 kites cost? (a) ₹75 (b) ₹194 (c) ₹50 (d) ₹400
20. 20.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
21. 21.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
22. 22.If 4 pens cost ₹16, how much do 7 pens cost? (a) ₹19 (b) ₹112 (c) ₹32 (d) ₹28
23. 23.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 3 days (d) 27 days
24. 24.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹12 (c) ₹18 (d) ₹24
25. 25.If 9 pens cost ₹81, how much do 3 pens cost? (a) ₹36 (b) ₹243 (c) ₹75 (d) ₹27
26. 26.₹250 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹175 (b) ₹25 (c) ₹125 (d) ₹75
27. 27.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹315 (d) ₹360
28. 28.9 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) 19 days (d) 39 days
29. 29.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 13 days (d) 14 days
30. 30.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹147 (d) ₹189
31. 31.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 2 days (d) 11 days
32. 32.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 5 days (d) 4 days
33. 33.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
34. 34.If 4 notebooks cost ₹32, how much do 10 notebooks cost? (a) ₹320 (b) ₹38 (c) ₹80 (d) ₹88
35. 35.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹75 (d) ₹25
36. 36.If 4 notebooks cost ₹88, how much do 10 notebooks cost? (a) ₹220 (b) ₹94 (c) ₹880 (d) ₹242
37. 37.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹82 (b) ₹41 (c) ₹123 (d) ₹164
38. 38.If 3 pens cost ₹48, how much do 2 pens cost? (a) ₹48 (b) ₹47 (c) ₹32 (d) ₹96
39. 39.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 4 days (d) 12 days
40. 40.If 9 notebooks cost ₹108, how much do 7 notebooks cost? (a) ₹96 (b) ₹84 (c) ₹756 (d) ₹106

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