Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 217 · 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 4 notebooks cost ₹96, how much do 5 notebooks cost? (a) ₹120 (b) ₹144 (c) ₹97 (d) ₹480
2. 2.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 2 days (d) 9 days
3. 3.If 8 pens cost ₹160, how much do 3 pens cost? (a) ₹80 (b) ₹155 (c) ₹480 (d) ₹60
4. 4.If 9 mangoes cost ₹144, how much do 4 mangoes cost? (a) ₹64 (b) ₹139 (c) ₹80 (d) ₹576
5. 5.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹35 (c) ₹175 (d) ₹210
6. 6.If 9 mangoes cost ₹162, how much do 11 mangoes cost? (a) ₹1782 (b) ₹198 (c) ₹216 (d) ₹164
7. 7.If 8 kites cost ₹176, how much do 5 kites cost? (a) ₹110 (b) ₹173 (c) ₹132 (d) ₹880
8. 8.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 9 days
9. 9.If 4 notebooks cost ₹20, how much do 12 notebooks cost? (a) ₹60 (b) ₹240 (c) ₹28 (d) ₹65
10. 10.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹165 (b) ₹231 (c) ₹33 (d) ₹297
11. 11.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹72 (c) ₹42 (d) ₹12
12. 12.If 5 pens cost ₹105, how much do 6 pens cost? (a) ₹630 (b) ₹147 (c) ₹106 (d) ₹126
13. 13.If 9 mangoes cost ₹135, how much do 8 mangoes cost? (a) ₹1080 (b) ₹120 (c) ₹135 (d) ₹134
14. 14.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 2 days (d) 11 days
15. 15.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 15 days (d) 5 days
16. 16.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 8 days
17. 17.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
18. 18.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹60 (d) ₹35
19. 19.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹240 (b) ₹192 (c) ₹48 (d) ₹216
20. 20.₹60 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹30 (d) ₹60
21. 21.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 7 days (d) 5 days
22. 22.₹132 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹132 (b) ₹33 (c) ₹99 (d) ₹66
23. 23.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹144 (c) ₹168 (d) ₹24
24. 24.If 8 pens cost ₹40, how much do 3 pens cost? (a) ₹35 (b) ₹120 (c) ₹20 (d) ₹15
25. 25.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹235 (c) ₹47 (d) ₹376
26. 26.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 12 days (d) 4 days
27. 27.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹141 (b) ₹35 (c) ₹175 (d) ₹140
28. 28.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹70 (b) ₹56 (c) ₹63 (d) ₹14
29. 29.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹55 (d) ₹44
30. 30.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 2 days (d) 3 days
31. 31.₹70 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹49 (b) ₹7 (c) ₹35 (d) ₹21
32. 32.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 9 days
33. 33.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 4 days (d) 8 days
34. 34.If 2 notebooks cost ₹10, how much do 4 notebooks cost? (a) ₹40 (b) ₹12 (c) ₹20 (d) ₹25
35. 35.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 9 days (d) 10 days
36. 36.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹13 (b) ₹16 (c) ₹48 (d) ₹20
37. 37.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 28 days (d) 11 days
38. 38.If 3 kites cost ₹21, how much do 10 kites cost? (a) ₹28 (b) ₹70 (c) ₹77 (d) ₹210
39. 39.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹54 (d) ₹42
40. 40.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 6 days

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