Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 930 · 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.₹154 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹28 (b) ₹77 (c) ₹126 (d) ₹14
2. 2.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 16 days (d) 1 day
3. 3.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹138 (b) ₹230 (c) ₹184 (d) ₹46
4. 4.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 11 days
5. 5.If 2 pens cost ₹46, how much do 3 pens cost? (a) ₹47 (b) ₹92 (c) ₹138 (d) ₹69
6. 6.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹175 (c) ₹250 (d) ₹50
7. 7.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 42 days (b) 8 days (c) 20 days (d) 43 days
8. 8.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 16 days
9. 9.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹117 (d) ₹91
10. 10.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹62 (b) ₹93 (c) ₹31 (d) ₹124
11. 11.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹12 (b) ₹27 (c) ₹42 (d) ₹6
12. 12.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹25 (b) ₹250 (c) ₹225 (d) ₹100
13. 13.₹120 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹96 (c) ₹60 (d) ₹24
14. 14.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹30 (c) ₹90 (d) ₹150
15. 15.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹8 (d) ₹36
16. 16.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 13 days (d) 11 days
17. 17.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 33 days (d) 14 days
18. 18.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹209 (b) ₹304 (c) ₹38 (d) ₹114
19. 19.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹299 (b) ₹184 (c) ₹414 (d) ₹46
20. 20.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 4 days
21. 21.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 13 days
22. 22.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
23. 23.If 7 mangoes cost ₹126, how much do 6 mangoes cost? (a) ₹125 (b) ₹108 (c) ₹756 (d) ₹126
24. 24.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 13 days (c) 1 day (d) 16 days
25. 25.If 8 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹672 (b) ₹60 (c) ₹91 (d) ₹84
26. 26.If 5 notebooks cost ₹125, how much do 2 notebooks cost? (a) ₹50 (b) ₹75 (c) ₹122 (d) ₹250
27. 27.If 6 mangoes cost ₹120, how much do 5 mangoes cost? (a) ₹600 (b) ₹100 (c) ₹120 (d) ₹119
28. 28.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹26 (b) ₹143 (c) ₹104 (d) ₹182
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
30. 30.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 13 days (d) 11 days
31. 31.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹325 (b) ₹250 (c) ₹400 (d) ₹50
32. 32.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 15 days (d) 13 days
33. 33.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹98 (b) ₹56 (c) ₹112 (d) ₹14
34. 34.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹25 (c) ₹5 (d) ₹45
35. 35.If 8 kites cost ₹48, how much do 11 kites cost? (a) ₹51 (b) ₹66 (c) ₹72 (d) ₹528
36. 36.If 3 kites cost ₹36, how much do 9 kites cost? (a) ₹42 (b) ₹108 (c) ₹324 (d) ₹120
37. 37.If 5 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹168 (b) ₹122 (c) ₹840 (d) ₹192
38. 38.If 5 notebooks cost ₹110, how much do 6 notebooks cost? (a) ₹660 (b) ₹154 (c) ₹132 (d) ₹111
39. 39.If 8 pens cost ₹80, how much do 3 pens cost? (a) ₹75 (b) ₹30 (c) ₹40 (d) ₹240
40. 40.₹56 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹48 (b) ₹56 (c) ₹28 (d) ₹8

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