Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 348 · 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 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 15 days (d) 2 days
2. 2.If 2 kites cost ₹16, how much do 3 kites cost? (a) ₹24 (b) ₹17 (c) ₹48 (d) ₹32
3. 3.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
4. 4.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 10 days (d) 16 days
5. 5.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹27 (c) ₹81 (d) ₹55
6. 6.If 9 notebooks cost ₹126, how much do 12 notebooks cost? (a) ₹129 (b) ₹182 (c) ₹168 (d) ₹1512
7. 7.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹273 (b) ₹42 (c) ₹168 (d) ₹378
8. 8.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 5 days (c) 15 days (d) 35 days
9. 9.7 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) 13 days (d) 14 days
10. 10.If 5 notebooks cost ₹15, how much do 6 notebooks cost? (a) ₹18 (b) ₹21 (c) ₹90 (d) ₹16
11. 11.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹273 (b) ₹210 (c) ₹336 (d) ₹42
12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 7 days (d) 8 days
13. 13.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹176 (d) ₹198
14. 14.If 6 kites cost ₹66, how much do 12 kites cost? (a) ₹143 (b) ₹72 (c) ₹132 (d) ₹792
15. 15.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹39 (d) ₹65
16. 16.If 3 kites cost ₹75, how much do 5 kites cost? (a) ₹125 (b) ₹77 (c) ₹150 (d) ₹375
17. 17.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 6 days (d) 8 days
18. 18.₹264 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹264 (b) ₹231 (c) ₹33 (d) ₹132
19. 19.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹54 (b) ₹81 (c) ₹27 (d) ₹108
20. 20.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹61 (b) ₹300 (c) ₹90 (d) ₹75
21. 21.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 19 days (b) 16 days (c) 18 days (d) 12 days
22. 22.If 9 pens cost ₹117, how much do 5 pens cost? (a) ₹113 (b) ₹585 (c) ₹65 (d) ₹78
23. 23.If 6 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹55 (b) ₹34 (c) ₹300 (d) ₹50
24. 24.If 6 mangoes cost ₹102, how much do 7 mangoes cost? (a) ₹714 (b) ₹119 (c) ₹136 (d) ₹103
25. 25.If 4 pens cost ₹36, how much do 8 pens cost? (a) ₹288 (b) ₹81 (c) ₹40 (d) ₹72
26. 26.₹385 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹280 (b) ₹35 (c) ₹245 (d) ₹140
27. 27.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 20 days (d) 21 days
28. 28.If 7 mangoes cost ₹126, how much do 8 mangoes cost? (a) ₹1008 (b) ₹127 (c) ₹144 (d) ₹162
29. 29.3 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) 4 days (d) 11 days
30. 30.If 8 pens cost ₹112, how much do 7 pens cost? (a) ₹111 (b) ₹112 (c) ₹98 (d) ₹784
31. 31.If 5 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹24 (b) ₹28 (c) ₹120 (d) ₹21
32. 32.If 7 notebooks cost ₹175, how much do 9 notebooks cost? (a) ₹1575 (b) ₹225 (c) ₹250 (d) ₹177
33. 33.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 13 days (d) 5 days
34. 34.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹42 (d) ₹43
35. 35.If 2 notebooks cost ₹48, how much do 8 notebooks cost? (a) ₹54 (b) ₹216 (c) ₹384 (d) ₹192
36. 36.If 5 mangoes cost ₹105, how much do 6 mangoes cost? (a) ₹106 (b) ₹147 (c) ₹126 (d) ₹630
37. 37.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 3 days
38. 38.If 2 kites cost ₹44, how much do 5 kites cost? (a) ₹132 (b) ₹220 (c) ₹110 (d) ₹47
39. 39.If 2 notebooks cost ₹34, how much do 5 notebooks cost? (a) ₹37 (b) ₹85 (c) ₹102 (d) ₹170
40. 40.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 19 days (c) 6 days (d) 18 days

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