Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 262 · 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.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹44 (d) ₹88
2. 2.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹180 (b) ₹36 (c) ₹108 (d) ₹252
3. 3.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 2 days (d) 12 days
4. 4.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 11 days (d) 19 days
5. 5.If 5 kites cost ₹25, how much do 11 kites cost? (a) ₹55 (b) ₹31 (c) ₹60 (d) ₹275
6. 6.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹204 (b) ₹34 (c) ₹238 (d) ₹170
7. 7.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 15 days (d) 5 days
8. 8.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 22 days (d) 23 days
9. 9.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹325 (b) ₹50 (c) ₹200 (d) ₹450
10. 10.If 7 pens cost ₹28, how much do 2 pens cost? (a) ₹23 (b) ₹56 (c) ₹8 (d) ₹12
11. 11.If 2 pens cost ₹24, how much do 7 pens cost? (a) ₹96 (b) ₹29 (c) ₹84 (d) ₹168
12. 12.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹165 (b) ₹231 (c) ₹99 (d) ₹33
13. 13.If 8 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹9 (b) ₹72 (c) ₹12 (d) ₹19
14. 14.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹105 (b) ₹120 (c) ₹15 (d) ₹30
15. 15.If 6 pens cost ₹108, how much do 7 pens cost? (a) ₹126 (b) ₹756 (c) ₹109 (d) ₹144
16. 16.If 4 notebooks cost ₹92, how much do 3 notebooks cost? (a) ₹92 (b) ₹276 (c) ₹91 (d) ₹69
17. 17.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 14 days (d) 20 days
18. 18.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹304 (b) ₹38 (c) ₹190 (d) ₹247
19. 19.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹312 (b) ₹156 (c) ₹273 (d) ₹39
20. 20.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 30 days (d) 31 days
21. 21.If 3 notebooks cost ₹21, how much do 6 notebooks cost? (a) ₹42 (b) ₹24 (c) ₹126 (d) ₹49
22. 22.If 6 kites cost ₹18, how much do 10 kites cost? (a) ₹180 (b) ₹22 (c) ₹30 (d) ₹33
23. 23.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹100 (c) ₹20 (d) ₹60
24. 24.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 2 days (d) 6 days
25. 25.If 2 mangoes cost ₹6, how much do 8 mangoes cost? (a) ₹48 (b) ₹24 (c) ₹27 (d) ₹12
26. 26.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹173 (d) ₹172
27. 27.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹350 (d) ₹250
28. 28.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹71 (d) ₹35
29. 29.₹429 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹312 (b) ₹351 (c) ₹117 (d) ₹39
30. 30.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹390 (d) ₹351
31. 31.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 11 days (d) 8 days
32. 32.If 7 kites cost ₹112, how much do 9 kites cost? (a) ₹144 (b) ₹114 (c) ₹1008 (d) ₹160
33. 33.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 6 days (d) 4 days
34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 3 days (d) 2 days
35. 35.If 4 pens cost ₹36, how much do 9 pens cost? (a) ₹324 (b) ₹41 (c) ₹81 (d) ₹90
36. 36.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹108 (b) ₹36 (c) ₹53 (d) ₹54
37. 37.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 13 days
38. 38.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 4 days (d) 49 days
39. 39.If 6 pens cost ₹54, how much do 3 pens cost? (a) ₹51 (b) ₹162 (c) ₹36 (d) ₹27
40. 40.9 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 9 days (d) 8 days

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