Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 300 · 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.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹90 (c) ₹108 (d) ₹72
2. 2.If 5 notebooks cost ₹15, how much do 10 notebooks cost? (a) ₹30 (b) ₹20 (c) ₹33 (d) ₹150
3. 3.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 8 days (d) 6 days
4. 4.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days
5. 5.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 26 days (d) 9 days
6. 6.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹450 (b) ₹405 (c) ₹225 (d) ₹45
7. 7.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 7 days
8. 8.If 3 kites cost ₹18, how much do 12 kites cost? (a) ₹27 (b) ₹72 (c) ₹78 (d) ₹216
9. 9.If 2 kites cost ₹22, how much do 3 kites cost? (a) ₹23 (b) ₹33 (c) ₹66 (d) ₹44
10. 10.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 14 days (d) 10 days
11. 11.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 4 days
12. 12.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹162 (c) ₹72 (d) ₹252
13. 13.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹39 (c) ₹234 (d) ₹273
14. 14.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 8 days (d) 13 days
15. 15.₹468 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹273 (b) ₹195 (c) ₹39 (d) ₹234
16. 16.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹73 (d) ₹81
17. 17.If 8 kites cost ₹144, how much do 5 kites cost? (a) ₹141 (b) ₹90 (c) ₹720 (d) ₹108
18. 18.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹333 (d) ₹296
19. 19.If 9 kites cost ₹126, how much do 10 kites cost? (a) ₹154 (b) ₹1260 (c) ₹140 (d) ₹127
20. 20.₹250 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹125 (b) ₹250 (c) ₹25 (d) ₹225
21. 21.If 9 kites cost ₹153, how much do 7 kites cost? (a) ₹119 (b) ₹1071 (c) ₹151 (d) ₹136
22. 22.If 2 pens cost ₹10, how much do 3 pens cost? (a) ₹15 (b) ₹11 (c) ₹20 (d) ₹30
23. 23.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 6 days (d) 18 days
24. 24.If 9 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹180 (b) ₹40 (c) ₹20 (d) ₹25
25. 25.If 3 mangoes cost ₹66, how much do 5 mangoes cost? (a) ₹330 (b) ₹68 (c) ₹132 (d) ₹110
26. 26.If 6 mangoes cost ₹90, how much do 9 mangoes cost? (a) ₹810 (b) ₹93 (c) ₹135 (d) ₹150
27. 27.If 5 pens cost ₹40, how much do 3 pens cost? (a) ₹32 (b) ₹24 (c) ₹38 (d) ₹120
28. 28.4 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) 6 days (d) 2 days
29. 29.If 4 mangoes cost ₹80, how much do 6 mangoes cost? (a) ₹140 (b) ₹120 (c) ₹480 (d) ₹82
30. 30.If 3 pens cost ₹12, how much do 9 pens cost? (a) ₹18 (b) ₹108 (c) ₹40 (d) ₹36
31. 31.If 5 pens cost ₹90, how much do 11 pens cost? (a) ₹96 (b) ₹216 (c) ₹990 (d) ₹198
32. 32.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹145 (b) ₹117 (c) ₹29 (d) ₹116
33. 33.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
34. 34.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 8 days
35. 35.₹198 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹54 (c) ₹18 (d) ₹144
36. 36.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 5 days
37. 37.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 25 days (d) 24 days
38. 38.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹136 (b) ₹85 (c) ₹17 (d) ₹153
39. 39.If 3 mangoes cost ₹27, how much do 7 mangoes cost? (a) ₹72 (b) ₹31 (c) ₹63 (d) ₹189
40. 40.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 56 days (d) 20 days

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