Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 681 · 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 8 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 16 days (d) 4 days
2. 2.₹451 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹164 (b) ₹328 (c) ₹41 (d) ₹287
3. 3.If 5 pens cost ₹55, how much do 4 pens cost? (a) ₹44 (b) ₹55 (c) ₹54 (d) ₹220
4. 4.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹10 (b) ₹11 (c) ₹15 (d) ₹5
5. 5.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 14 days
6. 6.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹135 (b) ₹243 (c) ₹27 (d) ₹189
7. 7.If 4 kites cost ₹52, how much do 9 kites cost? (a) ₹57 (b) ₹468 (c) ₹117 (d) ₹130
8. 8.If 4 mangoes cost ₹68, how much do 5 mangoes cost? (a) ₹69 (b) ₹340 (c) ₹102 (d) ₹85
9. 9.If 4 pens cost ₹84, how much do 2 pens cost? (a) ₹63 (b) ₹42 (c) ₹168 (d) ₹82
10. 10.3 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) 27 days (d) 15 days
11. 11.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 3 days (d) 6 days
12. 12.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹387 (d) ₹344
13. 13.If 5 mangoes cost ₹15, how much do 3 mangoes cost? (a) ₹9 (b) ₹12 (c) ₹13 (d) ₹45
14. 14.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 14 days (d) 16 days
15. 15.If 2 pens cost ₹8, how much do 3 pens cost? (a) ₹12 (b) ₹24 (c) ₹9 (d) ₹16
16. 16.If 5 kites cost ₹15, how much do 4 kites cost? (a) ₹14 (b) ₹12 (c) ₹15 (d) ₹60
17. 17.If 9 notebooks cost ₹180, how much do 3 notebooks cost? (a) ₹80 (b) ₹174 (c) ₹540 (d) ₹60
18. 18.If 4 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹28 (b) ₹21 (c) ₹27 (d) ₹84
19. 19.If 4 notebooks cost ₹24, how much do 6 notebooks cost? (a) ₹26 (b) ₹144 (c) ₹42 (d) ₹36
20. 20.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 16 days (d) 13 days
21. 21.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 1 day
22. 22.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 22 days (d) 21 days
23. 23.If 5 mangoes cost ₹90, how much do 8 mangoes cost? (a) ₹162 (b) ₹720 (c) ₹144 (d) ₹93
24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
25. 25.If 6 pens cost ₹72, how much do 9 pens cost? (a) ₹75 (b) ₹120 (c) ₹108 (d) ₹648
26. 26.If 2 mangoes cost ₹8, how much do 10 mangoes cost? (a) ₹44 (b) ₹40 (c) ₹80 (d) ₹16
27. 27.If 5 pens cost ₹120, how much do 9 pens cost? (a) ₹240 (b) ₹1080 (c) ₹124 (d) ₹216
28. 28.₹126 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹63 (c) ₹126 (d) ₹84
29. 29.₹196 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹168 (d) ₹98
30. 30.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 11 days (d) 2 days
31. 31.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 12 days (d) 11 days
32. 32.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 9 days (d) 15 days
33. 33.If 5 mangoes cost ₹95, how much do 6 mangoes cost? (a) ₹133 (b) ₹114 (c) ₹96 (d) ₹570
34. 34.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹5 (d) ₹25
35. 35.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹230 (b) ₹184 (c) ₹46 (d) ₹207
36. 36.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 17 days (d) 11 days
37. 37.If 9 pens cost ₹54, how much do 8 pens cost? (a) ₹53 (b) ₹54 (c) ₹432 (d) ₹48
38. 38.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹270 (b) ₹243 (c) ₹27 (d) ₹108
39. 39.If 4 notebooks cost ₹56, how much do 5 notebooks cost? (a) ₹84 (b) ₹57 (c) ₹70 (d) ₹280
40. 40.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days

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