Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 505 · 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 3 notebooks cost ₹45, how much do 12 notebooks cost? (a) ₹195 (b) ₹180 (c) ₹540 (d) ₹54
2. 2.If 3 pens cost ₹54, how much do 7 pens cost? (a) ₹144 (b) ₹126 (c) ₹378 (d) ₹58
3. 3.If 3 kites cost ₹54, how much do 6 kites cost? (a) ₹108 (b) ₹57 (c) ₹126 (d) ₹324
4. 4.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 15 days (d) 11 days
5. 5.₹637 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹196 (b) ₹441 (c) ₹49 (d) ₹490
6. 6.If 3 mangoes cost ₹9, how much do 9 mangoes cost? (a) ₹81 (b) ₹30 (c) ₹27 (d) ₹15
7. 7.If 9 mangoes cost ₹126, how much do 7 mangoes cost? (a) ₹98 (b) ₹112 (c) ₹124 (d) ₹882
8. 8.If 6 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹18 (b) ₹24 (c) ₹108 (d) ₹33
9. 9.If 9 kites cost ₹54, how much do 10 kites cost? (a) ₹66 (b) ₹540 (c) ₹55 (d) ₹60
10. 10.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 17 days (d) 22 days
11. 11.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 11 days (d) 9 days
12. 12.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹57 (d) ₹7
13. 13.If 5 pens cost ₹30, how much do 2 pens cost? (a) ₹60 (b) ₹18 (c) ₹27 (d) ₹12
14. 14.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹328 (b) ₹82 (c) ₹41 (d) ₹287
15. 15.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 10 days (d) 16 days
16. 16.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 15 days (c) 3 days (d) 27 days
17. 17.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 21 days (c) 48 days (d) 4 days
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
19. 19.If 2 kites cost ₹28, how much do 7 kites cost? (a) ₹196 (b) ₹112 (c) ₹33 (d) ₹98
20. 20.If 9 notebooks cost ₹207, how much do 4 notebooks cost? (a) ₹828 (b) ₹202 (c) ₹115 (d) ₹92
21. 21.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 14 days
22. 22.If 8 kites cost ₹152, how much do 12 kites cost? (a) ₹247 (b) ₹1824 (c) ₹156 (d) ₹228
23. 23.If 2 mangoes cost ₹28, how much do 10 mangoes cost? (a) ₹140 (b) ₹280 (c) ₹154 (d) ₹36
24. 24.If 7 mangoes cost ₹70, how much do 6 mangoes cost? (a) ₹70 (b) ₹69 (c) ₹420 (d) ₹60
25. 25.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 7 days
26. 26.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹165 (b) ₹150 (c) ₹30 (d) ₹180
27. 27.If 3 pens cost ₹75, how much do 10 pens cost? (a) ₹750 (b) ₹275 (c) ₹82 (d) ₹250
28. 28.If 8 pens cost ₹144, how much do 4 pens cost? (a) ₹140 (b) ₹576 (c) ₹90 (d) ₹72
29. 29.If 6 pens cost ₹144, how much do 11 pens cost? (a) ₹264 (b) ₹288 (c) ₹1584 (d) ₹149
30. 30.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹225 (b) ₹200 (c) ₹250 (d) ₹50
31. 31.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 17 days (d) 13 days
32. 32.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹225 (b) ₹50 (c) ₹250 (d) ₹25
33. 33.If 4 mangoes cost ₹100, how much do 5 mangoes cost? (a) ₹500 (b) ₹125 (c) ₹150 (d) ₹101
34. 34.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 7 days (c) 33 days (d) 15 days
35. 35.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 14 days (d) 13 days
36. 36.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹72 (b) ₹18 (c) ₹144 (d) ₹126
37. 37.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 27 days (d) 13 days
38. 38.If 3 kites cost ₹48, how much do 6 kites cost? (a) ₹288 (b) ₹51 (c) ₹112 (d) ₹96
39. 39.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 9 days (d) 8 days
40. 40.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹60 (b) ₹21 (c) ₹40 (d) ₹30

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