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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 307 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹13 (c) ₹104 (d) ₹65
  2. 2.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹64 (b) ₹8 (c) ₹32 (d) ₹56
  3. 3.If 5 kites cost ₹125, how much do 2 kites cost? (a) ₹75 (b) ₹50 (c) ₹122 (d) ₹250
  4. 4.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 34 days (c) 5 days (d) 17 days
  5. 5.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 13 days (d) 2 days
  6. 6.If 6 pens cost ₹18, how much do 3 pens cost? (a) ₹9 (b) ₹54 (c) ₹15 (d) ₹12
  7. 7.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 20 days (d) 8 days
  8. 8.₹476 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹238 (d) ₹306
  9. 9.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 10 days (d) 11 days
  10. 10.If 3 notebooks cost ₹9, how much do 5 notebooks cost? (a) ₹45 (b) ₹11 (c) ₹15 (d) ₹18
  11. 11.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹290 (d) ₹261
  12. 12.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 18 days
  13. 13.If 4 kites cost ₹24, how much do 8 kites cost? (a) ₹48 (b) ₹28 (c) ₹54 (d) ₹192
  14. 14.If 8 pens cost ₹200, how much do 6 pens cost? (a) ₹1200 (b) ₹175 (c) ₹198 (d) ₹150
  15. 15.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹11 (d) ₹66
  16. 16.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹55 (b) ₹66 (c) ₹11 (d) ₹22
  17. 17.If 9 mangoes cost ₹81, how much do 10 mangoes cost? (a) ₹82 (b) ₹810 (c) ₹99 (d) ₹90
  18. 18.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 1 day (d) 2 days
  19. 19.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 16 days (d) 14 days
  20. 20.If 4 notebooks cost ₹32, how much do 10 notebooks cost? (a) ₹88 (b) ₹38 (c) ₹320 (d) ₹80
  21. 21.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹40 (b) ₹160 (c) ₹200 (d) ₹180
  22. 22.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
  23. 23.If 4 kites cost ₹40, how much do 2 kites cost? (a) ₹38 (b) ₹20 (c) ₹80 (d) ₹30
  24. 24.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 30 days (c) 11 days (d) 31 days
  25. 25.If 4 pens cost ₹72, how much do 3 pens cost? (a) ₹54 (b) ₹71 (c) ₹72 (d) ₹216
  26. 26.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹120 (d) ₹100
  27. 27.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹78 (c) ₹65 (d) ₹26
  28. 28.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 4 days (d) 5 days
  29. 29.If 4 mangoes cost ₹32, how much do 11 mangoes cost? (a) ₹96 (b) ₹39 (c) ₹352 (d) ₹88
  30. 30.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 7 days (d) 8 days
  31. 31.If 8 notebooks cost ₹72, how much do 9 notebooks cost? (a) ₹73 (b) ₹81 (c) ₹648 (d) ₹90
  32. 32.₹351 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹39 (b) ₹351 (c) ₹312 (d) ₹313
  33. 33.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹22 (d) ₹44
  34. 34.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 15 days (d) 14 days
  35. 35.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 16 days (d) 10 days
  36. 36.If 7 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹504 (b) ₹47 (c) ₹78 (d) ₹72
  37. 37.If 7 kites cost ₹126, how much do 4 kites cost? (a) ₹72 (b) ₹123 (c) ₹504 (d) ₹90
  38. 38.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 5 days (c) 3 days (d) 13 days
  39. 39.5 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
  40. 40.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹5 (b) ₹10 (c) ₹40 (d) ₹35

Answer key

  1. ₹104
  2. ₹56
  3. ₹50
  4. 33 days
  5. 1 day
  6. ₹9
  7. 42 days
  8. ₹306
  9. 10 days
  10. ₹15
  11. ₹261
  12. 4 days
  13. ₹48
  14. ₹150
  15. ₹55
  16. ₹55
  17. ₹90
  18. 2 days
  19. 16 days
  20. ₹80
  21. ₹200
  22. 3 days
  23. ₹20
  24. 30 days
  25. ₹54
  26. ₹100
  27. ₹78
  28. 4 days
  29. ₹88
  30. 7 days
  31. ₹81
  32. ₹312
  33. ₹33
  34. 14 days
  35. 16 days
  36. ₹72
  37. ₹72
  38. 27 days
  39. 4 days
  40. ₹35

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