Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 695 · 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. 1.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
2. 2.If 6 notebooks cost ₹84, how much do 7 notebooks cost? (a) ₹588 (b) ₹85 (c) ₹112 (d) ₹98
3. 3.If 2 pens cost ₹28, how much do 5 pens cost? (a) ₹84 (b) ₹140 (c) ₹31 (d) ₹70
4. 4.7 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
5. 5.If 7 mangoes cost ₹140, how much do 11 mangoes cost? (a) ₹1540 (b) ₹144 (c) ₹220 (d) ₹240
6. 6.If 5 kites cost ₹35, how much do 6 kites cost? (a) ₹42 (b) ₹49 (c) ₹36 (d) ₹210
7. 7.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹145 (d) ₹174
8. 8.₹55 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹35 (d) ₹30
9. 9.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹144 (d) ₹104
10. 10.If 7 mangoes cost ₹49, how much do 8 mangoes cost? (a) ₹63 (b) ₹56 (c) ₹50 (d) ₹392
11. 11.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 2 days (d) 16 days
12. 12.₹90 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹72 (b) ₹45 (c) ₹90 (d) ₹18
13. 13.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹144 (d) ₹180
14. 14.If 7 mangoes cost ₹161, how much do 3 mangoes cost? (a) ₹483 (b) ₹157 (c) ₹69 (d) ₹92
15. 15.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹72 (d) ₹24
16. 16.₹128 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹128 (d) ₹112
17. 17.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹270 (d) ₹225
18. 18.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 11 days (d) 45 days
19. 19.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹162 (b) ₹189 (c) ₹163 (d) ₹27
20. 20.If 4 pens cost ₹100, how much do 9 pens cost? (a) ₹105 (b) ₹900 (c) ₹250 (d) ₹225
21. 21.If 7 pens cost ₹63, how much do 11 pens cost? (a) ₹99 (b) ₹108 (c) ₹693 (d) ₹67
22. 22.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹143 (d) ₹234
23. 23.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹252 (b) ₹180 (c) ₹216 (d) ₹36
24. 24.If 5 kites cost ₹100, how much do 4 kites cost? (a) ₹99 (b) ₹400 (c) ₹80 (d) ₹100
25. 25.If 7 kites cost ₹147, how much do 2 kites cost? (a) ₹63 (b) ₹142 (c) ₹42 (d) ₹294
26. 26.If 5 notebooks cost ₹85, how much do 3 notebooks cost? (a) ₹255 (b) ₹83 (c) ₹68 (d) ₹51
27. 27.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹273 (b) ₹234 (c) ₹39 (d) ₹195
28. 28.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹156 (b) ₹78 (c) ₹117 (d) ₹39
29. 29.If 7 pens cost ₹77, how much do 10 pens cost? (a) ₹121 (b) ₹80 (c) ₹110 (d) ₹770
30. 30.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹28 (d) ₹70
31. 31.If 4 kites cost ₹60, how much do 5 kites cost? (a) ₹61 (b) ₹75 (c) ₹90 (d) ₹300
32. 32.₹168 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹168 (d) ₹84
33. 33.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 15 days (d) 10 days
34. 34.If 9 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹252 (b) ₹35 (c) ₹58 (d) ₹28
35. 35.If 7 mangoes cost ₹105, how much do 4 mangoes cost? (a) ₹75 (b) ₹420 (c) ₹60 (d) ₹102
36. 36.If 3 notebooks cost ₹24, how much do 10 notebooks cost? (a) ₹31 (b) ₹88 (c) ₹80 (d) ₹240
37. 37.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 10 days (d) 18 days
38. 38.If 4 pens cost ₹64, how much do 11 pens cost? (a) ₹704 (b) ₹71 (c) ₹192 (d) ₹176
39. 39.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 15 days (d) 14 days
40. 40.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 26 days (c) 27 days (d) 17 days

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