Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 706 · 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 2 kites cost ₹6, how much do 10 kites cost? (a) ₹14 (b) ₹30 (c) ₹60 (d) ₹33
2. 2.₹369 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹205 (b) ₹41 (c) ₹164 (d) ₹246
3. 3.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹31 (b) ₹124 (c) ₹186 (d) ₹155
4. 4.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹27 (c) ₹26 (d) ₹13
5. 5.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹27 (d) ₹18
6. 6.₹450 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹225 (d) ₹350
7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 27 days (d) 26 days
8. 8.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹304 (b) ₹38 (c) ₹152 (d) ₹266
9. 9.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 33 days (c) 17 days (d) 34 days
10. 10.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 4 days (d) 25 days
11. 11.If 7 kites cost ₹35, how much do 6 kites cost? (a) ₹35 (b) ₹210 (c) ₹30 (d) ₹34
12. 12.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹39 (b) ₹117 (c) ₹78 (d) ₹156
13. 13.If 6 notebooks cost ₹120, how much do 7 notebooks cost? (a) ₹121 (b) ₹840 (c) ₹140 (d) ₹160
14. 14.If 2 mangoes cost ₹48, how much do 3 mangoes cost? (a) ₹49 (b) ₹96 (c) ₹144 (d) ₹72
15. 15.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹32 (b) ₹112 (c) ₹224 (d) ₹192
16. 16.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 15 days (d) 27 days
17. 17.If 8 mangoes cost ₹32, how much do 11 mangoes cost? (a) ₹35 (b) ₹48 (c) ₹352 (d) ₹44
18. 18.If 4 mangoes cost ₹92, how much do 8 mangoes cost? (a) ₹96 (b) ₹736 (c) ₹184 (d) ₹207
19. 19.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 6 days (d) 4 days
20. 20.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹90 (d) ₹120
21. 21.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 8 days (d) 6 days
22. 22.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 7 days (d) 9 days
23. 23.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 6 days (d) 20 days
24. 24.If 6 kites cost ₹78, how much do 7 kites cost? (a) ₹91 (b) ₹79 (c) ₹104 (d) ₹546
25. 25.If 8 pens cost ₹32, how much do 9 pens cost? (a) ₹40 (b) ₹36 (c) ₹33 (d) ₹288
26. 26.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 2 days (d) 3 days
27. 27.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹60 (c) ₹108 (d) ₹12
28. 28.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹65 (b) ₹10 (c) ₹90 (d) ₹40
29. 29.If 9 kites cost ₹72, how much do 7 kites cost? (a) ₹504 (b) ₹70 (c) ₹56 (d) ₹64
30. 30.If 2 kites cost ₹8, how much do 5 kites cost? (a) ₹20 (b) ₹24 (c) ₹40 (d) ₹11
31. 31.₹143 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹99 (b) ₹11 (c) ₹55 (d) ₹88
32. 32.If 6 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹74 (b) ₹108 (c) ₹576 (d) ₹96
33. 33.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 17 days (d) 5 days
34. 34.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹250 (c) ₹50 (d) ₹450
35. 35.If 3 mangoes cost ₹27, how much do 8 mangoes cost? (a) ₹72 (b) ₹81 (c) ₹32 (d) ₹216
36. 36.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 28 days (d) 16 days
37. 37.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 13 days (d) 12 days
38. 38.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 7 days (d) 5 days
39. 39.If 6 pens cost ₹144, how much do 8 pens cost? (a) ₹146 (b) ₹192 (c) ₹216 (d) ₹1152
40. 40.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days

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