Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 18 · 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 ₹16, how much do 7 pens cost? (a) ₹56 (b) ₹21 (c) ₹112 (d) ₹64
2. 2.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 13 days (c) 11 days (d) 8 days
3. 3.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹130 (b) ₹143 (c) ₹26 (d) ₹156
4. 4.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹141 (b) ₹140 (c) ₹175 (d) ₹35
5. 5.If 6 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹33 (b) ₹18 (c) ₹108 (d) ₹24
6. 6.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 7 days
7. 7.If 8 pens cost ₹160, how much do 4 pens cost? (a) ₹100 (b) ₹156 (c) ₹80 (d) ₹640
8. 8.If 9 mangoes cost ₹27, how much do 6 mangoes cost? (a) ₹24 (b) ₹21 (c) ₹162 (d) ₹18
9. 9.6 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) 10 days (d) 12 days
10. 10.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 11 days (d) 15 days
11. 11.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 18 days (d) 10 days
12. 12.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 27 days (d) 28 days
13. 13.If 3 pens cost ₹75, how much do 9 pens cost? (a) ₹250 (b) ₹81 (c) ₹675 (d) ₹225
14. 14.If 6 pens cost ₹96, how much do 10 pens cost? (a) ₹100 (b) ₹176 (c) ₹960 (d) ₹160
15. 15.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 1 day (d) 21 days
16. 16.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 26 days (c) 16 days (d) 27 days
17. 17.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 15 days (d) 3 days
18. 18.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 13 days (d) 8 days
19. 19.If 6 pens cost ₹30, how much do 3 pens cost? (a) ₹15 (b) ₹27 (c) ₹90 (d) ₹20
20. 20.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 18 days (d) 8 days
21. 21.If 4 mangoes cost ₹68, how much do 2 mangoes cost? (a) ₹66 (b) ₹34 (c) ₹136 (d) ₹51
22. 22.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹93 (b) ₹155 (c) ₹186 (d) ₹31
23. 23.If 9 kites cost ₹81, how much do 10 kites cost? (a) ₹810 (b) ₹99 (c) ₹90 (d) ₹82
24. 24.If 8 pens cost ₹32, how much do 5 pens cost? (a) ₹24 (b) ₹20 (c) ₹160 (d) ₹29
25. 25.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹45 (d) ₹37
26. 26.If 8 pens cost ₹112, how much do 6 pens cost? (a) ₹98 (b) ₹672 (c) ₹84 (d) ₹110
27. 27.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 16 days (d) 4 days
28. 28.If 6 kites cost ₹54, how much do 11 kites cost? (a) ₹99 (b) ₹108 (c) ₹59 (d) ₹594
29. 29.If 9 notebooks cost ₹126, how much do 11 notebooks cost? (a) ₹128 (b) ₹168 (c) ₹1386 (d) ₹154
30. 30.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹90 (b) ₹80 (c) ₹45 (d) ₹10
31. 31.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 9 days (d) 7 days
32. 32.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 9 days
33. 33.If 2 kites cost ₹10, how much do 3 kites cost? (a) ₹11 (b) ₹30 (c) ₹20 (d) ₹15
34. 34.If 6 mangoes cost ₹48, how much do 7 mangoes cost? (a) ₹56 (b) ₹64 (c) ₹49 (d) ₹336
35. 35.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹77 (d) ₹99
36. 36.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹25 (b) ₹250 (c) ₹100 (d) ₹225
37. 37.If 2 pens cost ₹32, how much do 4 pens cost? (a) ₹80 (b) ₹128 (c) ₹34 (d) ₹64
38. 38.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹54 (c) ₹39 (d) ₹6
39. 39.If 3 mangoes cost ₹24, how much do 6 mangoes cost? (a) ₹144 (b) ₹56 (c) ₹48 (d) ₹27
40. 40.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹144 (b) ₹108 (c) ₹36 (d) ₹126

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