Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 874 · 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. 1.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 1 day (c) 3 days (d) 11 days
2. 2.If 3 mangoes cost ₹63, how much do 7 mangoes cost? (a) ₹441 (b) ₹147 (c) ₹168 (d) ₹67
3. 3.If 9 mangoes cost ₹54, how much do 12 mangoes cost? (a) ₹648 (b) ₹72 (c) ₹78 (d) ₹57
4. 4.If 3 kites cost ₹63, how much do 6 kites cost? (a) ₹66 (b) ₹147 (c) ₹126 (d) ₹378
5. 5.If 2 pens cost ₹48, how much do 8 pens cost? (a) ₹54 (b) ₹384 (c) ₹192 (d) ₹216
6. 6.If 8 mangoes cost ₹128, how much do 7 mangoes cost? (a) ₹112 (b) ₹128 (c) ₹896 (d) ₹127
7. 7.If 6 pens cost ₹36, how much do 3 pens cost? (a) ₹33 (b) ₹108 (c) ₹24 (d) ₹18
8. 8.If 8 kites cost ₹24, how much do 5 kites cost? (a) ₹18 (b) ₹15 (c) ₹120 (d) ₹21
9. 9.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹104 (b) ₹16 (c) ₹64 (d) ₹144
10. 10.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹35 (d) ₹49
11. 11.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 1 day (d) 21 days
12. 12.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹40 (b) ₹41 (c) ₹5 (d) ₹45
13. 13.If 3 notebooks cost ₹18, how much do 4 notebooks cost? (a) ₹72 (b) ₹19 (c) ₹24 (d) ₹30
14. 14.If 3 pens cost ₹18, how much do 4 pens cost? (a) ₹30 (b) ₹24 (c) ₹19 (d) ₹72
15. 15.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹10 (c) ₹60 (d) ₹50
16. 16.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 11 days (d) 27 days
17. 17.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹24 (b) ₹192 (c) ₹132 (d) ₹72
18. 18.₹84 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹70 (d) ₹14
19. 19.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹63 (c) ₹9 (d) ₹45
20. 20.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 6 days (d) 8 days
21. 21.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹242 (c) ₹176 (d) ₹308
22. 22.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 18 days (c) 12 days (d) 10 days
23. 23.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 4 days (d) 5 days
24. 24.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹238 (b) ₹136 (c) ₹34 (d) ₹272
25. 25.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹137 (b) ₹136 (c) ₹17 (d) ₹153
26. 26.If 6 pens cost ₹126, how much do 3 pens cost? (a) ₹378 (b) ₹84 (c) ₹63 (d) ₹123
27. 27.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 16 days (d) 36 days
28. 28.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹47 (b) ₹470 (c) ₹423 (d) ₹188
29. 29.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 8 days (d) 6 days
30. 30.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 2 days (d) 3 days
31. 31.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹63 (d) ₹9
32. 32.If 3 mangoes cost ₹9, how much do 2 mangoes cost? (a) ₹6 (b) ₹8 (c) ₹18 (d) ₹9
33. 33.If 4 notebooks cost ₹88, how much do 3 notebooks cost? (a) ₹66 (b) ₹264 (c) ₹87 (d) ₹88
34. 34.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹115 (d) ₹69
35. 35.If 4 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹46 (b) ₹96 (c) ₹36 (d) ₹24
36. 36.If 3 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹40 (b) ₹48 (c) ₹120 (d) ₹26
37. 37.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 27 days (d) 26 days
38. 38.If 6 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹32 (b) ₹25 (c) ₹28 (d) ₹168
39. 39.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹280 (d) ₹120
40. 40.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 17 days (d) 7 days

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