Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 283 · 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 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 10 days
2. 2.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹80 (b) ₹200 (c) ₹40 (d) ₹140
3. 3.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹430 (b) ₹43 (c) ₹215 (d) ₹387
4. 4.If 9 kites cost ₹171, how much do 4 kites cost? (a) ₹95 (b) ₹684 (c) ₹166 (d) ₹76
5. 5.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹15 (b) ₹16 (c) ₹12 (d) ₹48
6. 6.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 23 days (d) 22 days
7. 7.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 13 days
8. 8.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹180 (b) ₹210 (c) ₹30 (d) ₹105
9. 9.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
10. 10.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹8 (b) ₹20 (c) ₹24 (d) ₹16
11. 11.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 19 days
12. 12.If 7 mangoes cost ₹84, how much do 2 mangoes cost? (a) ₹36 (b) ₹24 (c) ₹79 (d) ₹168
13. 13.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
14. 14.If 4 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹48 (b) ₹168 (c) ₹42 (d) ₹27
15. 15.If 3 mangoes cost ₹39, how much do 8 mangoes cost? (a) ₹117 (b) ₹312 (c) ₹44 (d) ₹104
16. 16.If 6 kites cost ₹84, how much do 7 kites cost? (a) ₹112 (b) ₹588 (c) ₹98 (d) ₹85
17. 17.If 3 mangoes cost ₹21, how much do 10 mangoes cost? (a) ₹28 (b) ₹77 (c) ₹210 (d) ₹70
18. 18.If 8 mangoes cost ₹184, how much do 2 mangoes cost? (a) ₹69 (b) ₹368 (c) ₹178 (d) ₹46
19. 19.If 5 kites cost ₹55, how much do 10 kites cost? (a) ₹121 (b) ₹550 (c) ₹110 (d) ₹60
20. 20.If 4 kites cost ₹16, how much do 11 kites cost? (a) ₹23 (b) ₹176 (c) ₹48 (d) ₹44
21. 21.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 3 days (d) 4 days
22. 22.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
23. 23.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 11 days (d) 19 days
24. 24.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹24 (b) ₹144 (c) ₹120 (d) ₹72
25. 25.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 25 days (c) 12 days (d) 24 days
26. 26.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹36 (c) ₹180 (d) ₹216
27. 27.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 15 days (d) 7 days
28. 28.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 2 days
29. 29.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹44 (d) ₹22
30. 30.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹10 (c) ₹60 (d) ₹50
31. 31.₹270 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹135 (b) ₹270 (c) ₹45 (d) ₹225
32. 32.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹147 (d) ₹294
33. 33.If 3 notebooks cost ₹33, how much do 9 notebooks cost? (a) ₹110 (b) ₹99 (c) ₹39 (d) ₹297
34. 34.If 4 kites cost ₹40, how much do 6 kites cost? (a) ₹70 (b) ₹60 (c) ₹42 (d) ₹240
35. 35.If 4 pens cost ₹72, how much do 10 pens cost? (a) ₹78 (b) ₹180 (c) ₹720 (d) ₹198
36. 36.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹46 (c) ₹138 (d) ₹92
37. 37.₹126 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹18 (c) ₹54 (d) ₹72
38. 38.If 3 kites cost ₹30, how much do 10 kites cost? (a) ₹100 (b) ₹300 (c) ₹110 (d) ₹37
39. 39.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹198 (b) ₹528 (c) ₹176 (d) ₹71
40. 40.₹418 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹114 (b) ₹209 (c) ₹304 (d) ₹38

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