Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 156 · 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. 1.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 11 days
2. 2.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 4 days
3. 3.If 3 kites cost ₹39, how much do 10 kites cost? (a) ₹143 (b) ₹130 (c) ₹46 (d) ₹390
4. 4.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days
5. 5.If 8 kites cost ₹128, how much do 7 kites cost? (a) ₹127 (b) ₹128 (c) ₹112 (d) ₹896
6. 6.If 7 mangoes cost ₹175, how much do 3 mangoes cost? (a) ₹75 (b) ₹100 (c) ₹171 (d) ₹525
7. 7.If 6 mangoes cost ₹18, how much do 7 mangoes cost? (a) ₹24 (b) ₹19 (c) ₹21 (d) ₹126
8. 8.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 22 days (d) 21 days
9. 9.If 3 pens cost ₹33, how much do 8 pens cost? (a) ₹88 (b) ₹264 (c) ₹38 (d) ₹99
10. 10.If 5 pens cost ₹65, how much do 10 pens cost? (a) ₹143 (b) ₹650 (c) ₹70 (d) ₹130
11. 11.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹164 (b) ₹410 (c) ₹369 (d) ₹41
12. 12.₹308 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹112 (b) ₹154 (c) ₹28 (d) ₹196
13. 13.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 21 days (d) 22 days
14. 14.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 28 days (d) 10 days
15. 15.₹315 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹45 (b) ₹270 (c) ₹315 (d) ₹271
16. 16.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 13 days (d) 3 days
17. 17.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 15 days (d) 17 days
18. 18.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days
19. 19.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹50 (b) ₹60 (c) ₹10 (d) ₹30
20. 20.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹153 (d) ₹119
21. 21.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹30 (b) ₹48 (c) ₹12 (d) ₹60
22. 22.If 8 mangoes cost ₹120, how much do 6 mangoes cost? (a) ₹118 (b) ₹105 (c) ₹90 (d) ₹720
23. 23.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 3 days
24. 24.If 9 pens cost ₹117, how much do 8 pens cost? (a) ₹936 (b) ₹117 (c) ₹104 (d) ₹116
25. 25.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹216 (b) ₹90 (c) ₹72 (d) ₹55
26. 26.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹42 (d) ₹35
27. 27.If 2 mangoes cost ₹44, how much do 3 mangoes cost? (a) ₹132 (b) ₹66 (c) ₹45 (d) ₹88
28. 28.₹287 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹82 (b) ₹246 (c) ₹205 (d) ₹41
29. 29.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 3 days
30. 30.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹45 (c) ₹30 (d) ₹15
31. 31.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹133 (b) ₹95 (c) ₹19 (d) ₹114
32. 32.If 9 kites cost ₹117, how much do 5 kites cost? (a) ₹65 (b) ₹78 (c) ₹113 (d) ₹585
33. 33.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹128 (c) ₹16 (d) ₹48
34. 34.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹84 (b) ₹29 (c) ₹42 (d) ₹56
35. 35.If 6 pens cost ₹24, how much do 4 pens cost? (a) ₹20 (b) ₹96 (c) ₹22 (d) ₹16
36. 36.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹119 (b) ₹17 (c) ₹136 (d) ₹68
37. 37.If 5 kites cost ₹85, how much do 6 kites cost? (a) ₹102 (b) ₹510 (c) ₹119 (d) ₹86
38. 38.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 15 days (d) 16 days
39. 39.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 14 days (d) 15 days
40. 40.If 2 pens cost ₹10, how much do 9 pens cost? (a) ₹45 (b) ₹17 (c) ₹50 (d) ₹90

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