Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 70 · 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.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹65 (d) ₹52
2. 2.If 8 mangoes cost ₹144, how much do 2 mangoes cost? (a) ₹288 (b) ₹54 (c) ₹138 (d) ₹36
3. 3.If 4 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹35 (b) ₹22 (c) ₹120 (d) ₹30
4. 4.If 4 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹252 (b) ₹84 (c) ₹83 (d) ₹63
5. 5.If 2 pens cost ₹44, how much do 10 pens cost? (a) ₹52 (b) ₹440 (c) ₹220 (d) ₹242
6. 6.If 4 pens cost ₹28, how much do 5 pens cost? (a) ₹29 (b) ₹140 (c) ₹35 (d) ₹42
7. 7.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 21 days (c) 20 days (d) 14 days
8. 8.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 11 days (d) 19 days
9. 9.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹73 (b) ₹81 (c) ₹9 (d) ₹72
10. 10.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 56 days (d) 20 days
11. 11.If 3 notebooks cost ₹63, how much do 7 notebooks cost? (a) ₹67 (b) ₹441 (c) ₹168 (d) ₹147
12. 12.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹22 (d) ₹23
13. 13.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹67 (b) ₹99 (c) ₹33 (d) ₹66
14. 14.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 9 days (d) 3 days
15. 15.If 2 mangoes cost ₹34, how much do 4 mangoes cost? (a) ₹136 (b) ₹68 (c) ₹85 (d) ₹36
16. 16.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 13 days
17. 17.If 2 pens cost ₹20, how much do 12 pens cost? (a) ₹120 (b) ₹130 (c) ₹240 (d) ₹30
18. 18.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 6 days (d) 7 days
19. 19.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 3 days (c) 45 days (d) 17 days
20. 20.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 6 days (d) 24 days
21. 21.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹70 (b) ₹40 (c) ₹55 (d) ₹10
22. 22.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 16 days (d) 8 days
23. 23.If 4 pens cost ₹68, how much do 3 pens cost? (a) ₹204 (b) ₹51 (c) ₹68 (d) ₹67
24. 24.If 3 mangoes cost ₹33, how much do 5 mangoes cost? (a) ₹165 (b) ₹55 (c) ₹35 (d) ₹66
25. 25.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 12 days (c) 25 days (d) 24 days
26. 26.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹238 (d) ₹306
27. 27.If 7 kites cost ₹112, how much do 3 kites cost? (a) ₹108 (b) ₹48 (c) ₹336 (d) ₹64
28. 28.If 4 kites cost ₹44, how much do 9 kites cost? (a) ₹396 (b) ₹49 (c) ₹110 (d) ₹99
29. 29.If 9 kites cost ₹81, how much do 12 kites cost? (a) ₹108 (b) ₹972 (c) ₹117 (d) ₹84
30. 30.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 2 days (c) 7 days (d) 6 days
31. 31.If 6 notebooks cost ₹120, how much do 10 notebooks cost? (a) ₹220 (b) ₹124 (c) ₹200 (d) ₹1200
32. 32.If 6 kites cost ₹54, how much do 8 kites cost? (a) ₹432 (b) ₹81 (c) ₹72 (d) ₹56
33. 33.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹123 (c) ₹205 (d) ₹164
34. 34.If 9 notebooks cost ₹162, how much do 2 notebooks cost? (a) ₹324 (b) ₹54 (c) ₹155 (d) ₹36
35. 35.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
36. 36.If 4 kites cost ₹16, how much do 6 kites cost? (a) ₹96 (b) ₹24 (c) ₹28 (d) ₹18
37. 37.If 6 notebooks cost ₹126, how much do 11 notebooks cost? (a) ₹252 (b) ₹231 (c) ₹1386 (d) ₹131
38. 38.If 7 pens cost ₹91, how much do 2 pens cost? (a) ₹182 (b) ₹86 (c) ₹26 (d) ₹39
39. 39.₹378 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹336 (b) ₹378 (c) ₹42 (d) ₹189
40. 40.If 3 pens cost ₹18, how much do 5 pens cost? (a) ₹20 (b) ₹30 (c) ₹90 (d) ₹36

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