Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 747 · 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 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 12 days
2. 2.If 6 mangoes cost ₹66, how much do 11 mangoes cost? (a) ₹71 (b) ₹726 (c) ₹121 (d) ₹132
3. 3.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹13 (d) ₹78
4. 4.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 19 days (d) 27 days
5. 5.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹149 (d) ₹37
6. 6.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 14 days (d) 3 days
7. 7.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹150 (b) ₹275 (c) ₹400 (d) ₹50
8. 8.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 6 days (d) 4 days
10. 10.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 13 days (d) 19 days
11. 11.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹20 (c) ₹100 (d) ₹60
12. 12.If 2 kites cost ₹10, how much do 7 kites cost? (a) ₹15 (b) ₹70 (c) ₹40 (d) ₹35
13. 13.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 6 days
14. 14.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹36 (d) ₹30
15. 15.₹240 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹120
16. 16.If 4 notebooks cost ₹12, how much do 11 notebooks cost? (a) ₹33 (b) ₹132 (c) ₹36 (d) ₹19
17. 17.If 2 notebooks cost ₹22, how much do 7 notebooks cost? (a) ₹27 (b) ₹88 (c) ₹77 (d) ₹154
18. 18.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 6 days (d) 19 days
19. 19.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 7 days
20. 20.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 17 days (d) 6 days
21. 21.If 2 pens cost ₹40, how much do 12 pens cost? (a) ₹50 (b) ₹240 (c) ₹260 (d) ₹480
22. 22.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 10 days (d) 2 days
23. 23.If 7 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹462 (b) ₹46 (c) ₹72 (d) ₹66
24. 24.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 21 days (d) 22 days
25. 25.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹35 (d) ₹71
26. 26.If 2 pens cost ₹34, how much do 4 pens cost? (a) ₹85 (b) ₹136 (c) ₹36 (d) ₹68
27. 27.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 34 days (d) 33 days
28. 28.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹36 (c) ₹33 (d) ₹6
29. 29.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹60 (c) ₹12 (d) ₹108
30. 30.If 7 mangoes cost ₹84, how much do 2 mangoes cost? (a) ₹168 (b) ₹79 (c) ₹36 (d) ₹24
31. 31.If 3 mangoes cost ₹33, how much do 11 mangoes cost? (a) ₹132 (b) ₹41 (c) ₹363 (d) ₹121
32. 32.If 9 notebooks cost ₹207, how much do 6 notebooks cost? (a) ₹204 (b) ₹138 (c) ₹161 (d) ₹1242
33. 33.If 4 notebooks cost ₹44, how much do 2 notebooks cost? (a) ₹33 (b) ₹42 (c) ₹88 (d) ₹22
34. 34.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹72 (d) ₹56
35. 35.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹117 (b) ₹156 (c) ₹78 (d) ₹39
36. 36.If 3 notebooks cost ₹66, how much do 5 notebooks cost? (a) ₹68 (b) ₹132 (c) ₹330 (d) ₹110
37. 37.If 5 notebooks cost ₹55, how much do 8 notebooks cost? (a) ₹440 (b) ₹99 (c) ₹88 (d) ₹58
38. 38.If 6 notebooks cost ₹102, how much do 7 notebooks cost? (a) ₹136 (b) ₹103 (c) ₹119 (d) ₹714
39. 39.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹78 (b) ₹273 (c) ₹312 (d) ₹39
40. 40.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹137 (d) ₹153

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