Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 766 · 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.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹48 (c) ₹8 (d) ₹44
2. 2.If 4 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹66 (b) ₹45 (c) ₹55 (d) ₹220
3. 3.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹80 (b) ₹96 (c) ₹16 (d) ₹112
4. 4.If 4 pens cost ₹72, how much do 12 pens cost? (a) ₹216 (b) ₹80 (c) ₹234 (d) ₹864
5. 5.₹99 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹66 (b) ₹67 (c) ₹33 (d) ₹99
6. 6.If 5 mangoes cost ₹65, how much do 11 mangoes cost? (a) ₹143 (b) ₹715 (c) ₹71 (d) ₹156
7. 7.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 9 days
8. 8.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 14 days (c) 4 days (d) 15 days
9. 9.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹180 (c) ₹150 (d) ₹30
10. 10.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹102 (c) ₹119 (d) ₹17
11. 11.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 5 days
12. 12.If 3 pens cost ₹51, how much do 7 pens cost? (a) ₹55 (b) ₹136 (c) ₹119 (d) ₹357
13. 13.If 3 pens cost ₹36, how much do 7 pens cost? (a) ₹96 (b) ₹252 (c) ₹40 (d) ₹84
14. 14.If 4 pens cost ₹68, how much do 9 pens cost? (a) ₹612 (b) ₹73 (c) ₹170 (d) ₹153
15. 15.If 3 kites cost ₹24, how much do 5 kites cost? (a) ₹40 (b) ₹48 (c) ₹26 (d) ₹120
16. 16.If 6 pens cost ₹42, how much do 2 pens cost? (a) ₹38 (b) ₹84 (c) ₹21 (d) ₹14
17. 17.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹14 (d) ₹28
18. 18.If 8 mangoes cost ₹192, how much do 4 mangoes cost? (a) ₹188 (b) ₹768 (c) ₹120 (d) ₹96
19. 19.If 6 notebooks cost ₹96, how much do 2 notebooks cost? (a) ₹32 (b) ₹192 (c) ₹48 (d) ₹92
20. 20.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 4 days (d) 5 days
21. 21.If 8 kites cost ₹168, how much do 10 kites cost? (a) ₹1680 (b) ₹231 (c) ₹210 (d) ₹170
22. 22.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹73 (d) ₹72
23. 23.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹60 (d) ₹75
24. 24.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 22 days (d) 21 days
25. 25.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 32 days (c) 17 days (d) 2 days
26. 26.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 21 days (c) 22 days (d) 11 days
27. 27.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 39 days (d) 19 days
28. 28.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹252 (d) ₹140
29. 29.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 37 days (c) 3 days (d) 36 days
30. 30.9 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) 27 days (d) 19 days
31. 31.If 3 mangoes cost ₹51, how much do 4 mangoes cost? (a) ₹68 (b) ₹52 (c) ₹204 (d) ₹85
32. 32.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹88 (d) ₹110
33. 33.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹378 (b) ₹210 (c) ₹42 (d) ₹294
34. 34.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹136 (b) ₹34 (c) ₹119 (d) ₹102
35. 35.If 3 notebooks cost ₹57, how much do 4 notebooks cost? (a) ₹95 (b) ₹228 (c) ₹58 (d) ₹76
36. 36.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 16 days (d) 5 days
37. 37.If 3 kites cost ₹24, how much do 6 kites cost? (a) ₹56 (b) ₹48 (c) ₹144 (d) ₹27
38. 38.If 8 kites cost ₹80, how much do 9 kites cost? (a) ₹81 (b) ₹100 (c) ₹720 (d) ₹90
39. 39.If 2 kites cost ₹10, how much do 3 kites cost? (a) ₹15 (b) ₹11 (c) ₹20 (d) ₹30
40. 40.If 9 pens cost ₹189, how much do 10 pens cost? (a) ₹231 (b) ₹1890 (c) ₹190 (d) ₹210

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