Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 787 · 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. 1.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 9 days (c) 17 days (d) 39 days
2. 2.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹54 (b) ₹45 (c) ₹9 (d) ₹27
3. 3.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 32 days (c) 14 days (d) 33 days
4. 4.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 8 days
5. 5.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 7 days (d) 16 days
6. 6.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 8 days
7. 7.If 7 kites cost ₹147, how much do 2 kites cost? (a) ₹142 (b) ₹42 (c) ₹294 (d) ₹63
8. 8.If 6 notebooks cost ₹108, how much do 11 notebooks cost? (a) ₹1188 (b) ₹113 (c) ₹198 (d) ₹216
9. 9.If 4 mangoes cost ₹76, how much do 5 mangoes cost? (a) ₹380 (b) ₹77 (c) ₹114 (d) ₹95
10. 10.If 9 mangoes cost ₹27, how much do 2 mangoes cost? (a) ₹20 (b) ₹54 (c) ₹9 (d) ₹6
11. 11.If 5 pens cost ₹30, how much do 9 pens cost? (a) ₹270 (b) ₹54 (c) ₹34 (d) ₹60
12. 12.If 6 pens cost ₹54, how much do 8 pens cost? (a) ₹81 (b) ₹432 (c) ₹56 (d) ₹72
13. 13.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹279 (d) ₹249
14. 14.If 3 mangoes cost ₹18, how much do 10 mangoes cost? (a) ₹60 (b) ₹25 (c) ₹66 (d) ₹180
15. 15.If 2 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹198 (b) ₹44 (c) ₹180 (d) ₹360
16. 16.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 5 days (c) 36 days (d) 15 days
17. 17.If 7 kites cost ₹119, how much do 6 kites cost? (a) ₹102 (b) ₹118 (c) ₹714 (d) ₹119
18. 18.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹126 (b) ₹77 (c) ₹28 (d) ₹14
19. 19.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 16 days (d) 11 days
20. 20.If 7 kites cost ₹175, how much do 10 kites cost? (a) ₹1750 (b) ₹275 (c) ₹250 (d) ₹178
21. 21.If 7 kites cost ₹42, how much do 8 kites cost? (a) ₹43 (b) ₹48 (c) ₹336 (d) ₹54
22. 22.If 2 notebooks cost ₹30, how much do 5 notebooks cost? (a) ₹90 (b) ₹150 (c) ₹33 (d) ₹75
23. 23.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 8 days (d) 2 days
24. 24.₹125 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹101 (b) ₹125 (c) ₹25 (d) ₹100
25. 25.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹360 (b) ₹40 (c) ₹320 (d) ₹180
26. 26.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹18 (c) ₹81 (d) ₹9
27. 27.If 2 mangoes cost ₹16, how much do 4 mangoes cost? (a) ₹40 (b) ₹18 (c) ₹32 (d) ₹64
28. 28.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 6 days (d) 5 days
29. 29.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹140 (b) ₹182 (c) ₹28 (d) ₹224
30. 30.If 7 pens cost ₹77, how much do 11 pens cost? (a) ₹847 (b) ₹121 (c) ₹81 (d) ₹132
31. 31.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
32. 32.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 15 days (d) 14 days
33. 33.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹195 (b) ₹240 (c) ₹30 (d) ₹150
34. 34.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹14 (b) ₹42 (c) ₹7 (d) ₹35
35. 35.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 26 days (d) 27 days
36. 36.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹25 (b) ₹216 (c) ₹27 (d) ₹30
37. 37.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹99 (d) ₹110
38. 38.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹58 (b) ₹29 (c) ₹145 (d) ₹174
39. 39.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 7 days
40. 40.If 4 pens cost ₹12, how much do 6 pens cost? (a) ₹18 (b) ₹72 (c) ₹14 (d) ₹21

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