Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 256 · 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 8 pens cost ₹88, how much do 12 pens cost? (a) ₹92 (b) ₹132 (c) ₹143 (d) ₹1056
2. 2.If 6 pens cost ₹48, how much do 11 pens cost? (a) ₹53 (b) ₹88 (c) ₹528 (d) ₹96
3. 3.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹18 (d) ₹90
4. 4.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹12 (b) ₹18 (c) ₹6 (d) ₹24
5. 5.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹42 (b) ₹189 (c) ₹168 (d) ₹210
6. 6.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹19 (b) ₹171 (c) ₹95 (d) ₹190
7. 7.₹500 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹500 (b) ₹50 (c) ₹450 (d) ₹250
8. 8.₹574 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹369 (b) ₹41 (c) ₹287 (d) ₹205
9. 9.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹55 (c) ₹10 (d) ₹20
10. 10.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
11. 11.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 4 days (d) 16 days
12. 12.If 9 mangoes cost ₹63, how much do 11 mangoes cost? (a) ₹693 (b) ₹65 (c) ₹84 (d) ₹77
13. 13.If 6 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹66 (b) ₹60 (c) ₹360 (d) ₹40
14. 14.₹319 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹116 (b) ₹232 (c) ₹29 (d) ₹203
15. 15.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 6 days (c) 13 days (d) 12 days
16. 16.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 14 days
17. 17.If 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹28 (b) ₹34 (c) ₹140 (d) ₹35
18. 18.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹185 (b) ₹111 (c) ₹37 (d) ₹259
19. 19.If 2 notebooks cost ₹46, how much do 10 notebooks cost? (a) ₹460 (b) ₹54 (c) ₹230 (d) ₹253
20. 20.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹120 (d) ₹75
21. 21.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 6 days (d) 8 days
22. 22.If 2 kites cost ₹28, how much do 3 kites cost? (a) ₹42 (b) ₹84 (c) ₹29 (d) ₹56
23. 23.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 15 days (d) 9 days
24. 24.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹9 (b) ₹27 (c) ₹36 (d) ₹45
25. 25.₹250 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹125 (c) ₹250 (d) ₹200
26. 26.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹180 (c) ₹45 (d) ₹135
27. 27.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹21 (b) ₹168 (c) ₹189 (d) ₹105
28. 28.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 5 days (d) 6 days
29. 29.If 5 notebooks cost ₹25, how much do 3 notebooks cost? (a) ₹75 (b) ₹15 (c) ₹20 (d) ₹23
30. 30.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹87 (b) ₹116 (c) ₹58 (d) ₹29
31. 31.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 4 days (d) 16 days
32. 32.If 2 pens cost ₹50, how much do 9 pens cost? (a) ₹57 (b) ₹225 (c) ₹250 (d) ₹450
33. 33.If 7 kites cost ₹35, how much do 12 kites cost? (a) ₹60 (b) ₹420 (c) ₹40 (d) ₹65
34. 34.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹30 (d) ₹36
35. 35.If 8 mangoes cost ₹56, how much do 9 mangoes cost? (a) ₹504 (b) ₹57 (c) ₹70 (d) ₹63
36. 36.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
37. 37.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 4 days (d) 17 days
38. 38.If 3 notebooks cost ₹51, how much do 12 notebooks cost? (a) ₹612 (b) ₹60 (c) ₹204 (d) ₹221
39. 39.If 4 notebooks cost ₹72, how much do 7 notebooks cost? (a) ₹504 (b) ₹144 (c) ₹75 (d) ₹126
40. 40.If 7 kites cost ₹112, how much do 11 kites cost? (a) ₹116 (b) ₹176 (c) ₹192 (d) ₹1232

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