Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 855 · 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. 1.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 28 days (d) 13 days
2. 2.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 7 days (d) 10 days
3. 3.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 3 days (c) 15 days (d) 9 days
4. 4.₹324 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹72 (b) ₹162 (c) ₹36 (d) ₹252
5. 5.3 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) 4 days (d) 15 days
6. 6.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 12 days (d) 14 days
7. 7.If 4 mangoes cost ₹40, how much do 7 mangoes cost? (a) ₹70 (b) ₹43 (c) ₹80 (d) ₹280
8. 8.If 2 pens cost ₹30, how much do 4 pens cost? (a) ₹75 (b) ₹60 (c) ₹32 (d) ₹120
9. 9.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 17 days (d) 32 days
10. 10.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹90 (d) ₹75
11. 11.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹396 (c) ₹440 (d) ₹44
12. 12.If 2 notebooks cost ₹32, how much do 12 notebooks cost? (a) ₹42 (b) ₹384 (c) ₹208 (d) ₹192
13. 13.If 8 notebooks cost ₹136, how much do 11 notebooks cost? (a) ₹204 (b) ₹139 (c) ₹187 (d) ₹1496
14. 14.If 6 notebooks cost ₹36, how much do 5 notebooks cost? (a) ₹180 (b) ₹30 (c) ₹36 (d) ₹35
15. 15.If 3 notebooks cost ₹18, how much do 11 notebooks cost? (a) ₹66 (b) ₹26 (c) ₹72 (d) ₹198
16. 16.If 6 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹120 (b) ₹23 (c) ₹24 (d) ₹20
17. 17.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 11 days (d) 13 days
18. 18.₹45 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹45 (c) ₹30 (d) ₹15
19. 19.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹135 (d) ₹120
20. 20.₹98 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹42 (b) ₹49 (c) ₹14 (d) ₹56
21. 21.If 3 notebooks cost ₹57, how much do 12 notebooks cost? (a) ₹66 (b) ₹684 (c) ₹247 (d) ₹228
22. 22.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹77 (b) ₹19 (c) ₹76 (d) ₹95
23. 23.If 5 pens cost ₹70, how much do 4 pens cost? (a) ₹280 (b) ₹56 (c) ₹69 (d) ₹70
24. 24.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹234 (d) ₹143
25. 25.If 9 mangoes cost ₹180, how much do 8 mangoes cost? (a) ₹160 (b) ₹179 (c) ₹180 (d) ₹1440
26. 26.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 13 days (d) 27 days
27. 27.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 22 days (c) 16 days (d) 21 days
28. 28.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹110 (b) ₹140 (c) ₹80 (d) ₹20
29. 29.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹25 (b) ₹225 (c) ₹125 (d) ₹200
30. 30.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 7 days (d) 4 days
31. 31.If 4 kites cost ₹60, how much do 5 kites cost? (a) ₹300 (b) ₹90 (c) ₹61 (d) ₹75
32. 32.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹252 (b) ₹58 (c) ₹35 (d) ₹28
33. 33.If 9 mangoes cost ₹63, how much do 10 mangoes cost? (a) ₹630 (b) ₹77 (c) ₹64 (d) ₹70
34. 34.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹84 (c) ₹98 (d) ₹14
35. 35.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹282 (b) ₹329 (c) ₹47 (d) ₹235
36. 36.If 8 pens cost ₹176, how much do 5 pens cost? (a) ₹132 (b) ₹173 (c) ₹880 (d) ₹110
37. 37.If 7 pens cost ₹49, how much do 12 pens cost? (a) ₹84 (b) ₹54 (c) ₹588 (d) ₹91
38. 38.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹256 (d) ₹208
39. 39.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 1 day (d) 2 days
40. 40.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹46 (b) ₹184 (c) ₹322 (d) ₹368

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad