Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 757 · 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.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹246 (b) ₹205 (c) ₹287 (d) ₹41
2. 2.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
3. 3.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹124 (b) ₹248 (c) ₹31 (d) ₹217
4. 4.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 5 days
5. 5.If 7 kites cost ₹161, how much do 10 kites cost? (a) ₹164 (b) ₹1610 (c) ₹253 (d) ₹230
6. 6.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 4 days
7. 7.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 19 days
8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 9 days (d) 17 days
9. 9.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹72 (d) ₹52
10. 10.If 4 pens cost ₹40, how much do 10 pens cost? (a) ₹110 (b) ₹400 (c) ₹100 (d) ₹46
11. 11.₹333 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹296 (b) ₹74 (c) ₹259 (d) ₹37
12. 12.If 6 notebooks cost ₹138, how much do 3 notebooks cost? (a) ₹414 (b) ₹69 (c) ₹92 (d) ₹135
13. 13.If 9 pens cost ₹90, how much do 12 pens cost? (a) ₹1080 (b) ₹130 (c) ₹120 (d) ₹93
14. 14.If 8 pens cost ₹56, how much do 3 pens cost? (a) ₹51 (b) ₹28 (c) ₹21 (d) ₹168
15. 15.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 7 days
16. 16.If 8 kites cost ₹176, how much do 2 kites cost? (a) ₹44 (b) ₹352 (c) ₹170 (d) ₹66
17. 17.If 7 pens cost ₹35, how much do 8 pens cost? (a) ₹36 (b) ₹45 (c) ₹280 (d) ₹40
18. 18.₹301 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹258 (b) ₹301 (c) ₹43 (d) ₹259
19. 19.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹37 (b) ₹333 (c) ₹370 (d) ₹74
20. 20.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹88 (b) ₹110 (c) ₹55 (d) ₹22
21. 21.If 3 kites cost ₹33, how much do 4 kites cost? (a) ₹44 (b) ₹132 (c) ₹34 (d) ₹55
22. 22.If 4 notebooks cost ₹88, how much do 6 notebooks cost? (a) ₹528 (b) ₹154 (c) ₹90 (d) ₹132
23. 23.₹270 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹135 (b) ₹225 (c) ₹270 (d) ₹45
24. 24.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 13 days (d) 16 days
25. 25.If 3 mangoes cost ₹42, how much do 7 mangoes cost? (a) ₹112 (b) ₹294 (c) ₹98 (d) ₹46
26. 26.If 3 mangoes cost ₹15, how much do 7 mangoes cost? (a) ₹35 (b) ₹19 (c) ₹105 (d) ₹40
27. 27.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 4 days
28. 28.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹100 (b) ₹76 (c) ₹300 (d) ₹125
29. 29.If 3 mangoes cost ₹12, how much do 10 mangoes cost? (a) ₹19 (b) ₹44 (c) ₹40 (d) ₹120
30. 30.6 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
31. 31.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 12 days (c) 24 days (d) 25 days
32. 32.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹44 (c) ₹40 (d) ₹48
33. 33.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹190 (b) ₹380 (c) ₹342 (d) ₹38
34. 34.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 3 days (d) 2 days
35. 35.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 14 days (c) 31 days (d) 6 days
36. 36.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹10 (c) ₹30 (d) ₹40
37. 37.If 4 pens cost ₹80, how much do 3 pens cost? (a) ₹79 (b) ₹60 (c) ₹240 (d) ₹80
38. 38.If 3 notebooks cost ₹30, how much do 6 notebooks cost? (a) ₹180 (b) ₹33 (c) ₹60 (d) ₹70
39. 39.₹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
40. 40.If 9 kites cost ₹153, how much do 10 kites cost? (a) ₹1530 (b) ₹154 (c) ₹170 (d) ₹187

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