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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 553 · 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.If 8 notebooks cost ₹176, how much do 9 notebooks cost? (a) ₹1584 (b) ₹177 (c) ₹220 (d) ₹198
  2. 2.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 24 days (b) 16 days (c) 8 days (d) 6 days
  3. 3.If 7 pens cost ₹84, how much do 5 pens cost? (a) ₹72 (b) ₹60 (c) ₹420 (d) ₹82
  4. 4.If 2 mangoes cost ₹18, how much do 9 mangoes cost? (a) ₹90 (b) ₹81 (c) ₹162 (d) ₹25
  5. 5.If 8 kites cost ₹192, how much do 2 kites cost? (a) ₹72 (b) ₹384 (c) ₹48 (d) ₹186
  6. 6.8 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) 8 days (d) 9 days
  7. 7.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 12 days (d) 8 days
  8. 8.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
  9. 9.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹370 (b) ₹37 (c) ₹74 (d) ₹333
  10. 10.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹81 (d) ₹90
  11. 11.If 3 notebooks cost ₹24, how much do 6 notebooks cost? (a) ₹56 (b) ₹27 (c) ₹144 (d) ₹48
  12. 12.If 3 pens cost ₹45, how much do 8 pens cost? (a) ₹135 (b) ₹120 (c) ₹360 (d) ₹50
  13. 13.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹141 (c) ₹175 (d) ₹140
  14. 14.3 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
  15. 15.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 6 days (d) 7 days
  16. 16.₹450 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹450 (b) ₹225 (c) ₹50 (d) ₹400
  17. 17.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 11 days (d) 21 days
  18. 18.If 6 kites cost ₹102, how much do 2 kites cost? (a) ₹51 (b) ₹34 (c) ₹204 (d) ₹98
  19. 19.If 5 notebooks cost ₹80, how much do 8 notebooks cost? (a) ₹128 (b) ₹640 (c) ₹83 (d) ₹144
  20. 20.If 5 kites cost ₹75, how much do 2 kites cost? (a) ₹30 (b) ₹150 (c) ₹72 (d) ₹45
  21. 21.If 5 pens cost ₹100, how much do 8 pens cost? (a) ₹103 (b) ₹160 (c) ₹800 (d) ₹180
  22. 22.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 9 days
  23. 23.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 7 days (d) 8 days
  24. 24.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 7 days (d) 16 days
  25. 25.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 7 days (d) 11 days
  26. 26.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 16 days (d) 12 days
  27. 27.If 5 notebooks cost ₹55, how much do 6 notebooks cost? (a) ₹330 (b) ₹56 (c) ₹77 (d) ₹66
  28. 28.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹340 (b) ₹306 (c) ₹170 (d) ₹34
  29. 29.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 41 days (b) 16 days (c) 40 days (d) 4 days
  30. 30.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹49 (c) ₹14 (d) ₹98
  31. 31.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 19 days (d) 40 days
  32. 32.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹129 (d) ₹172
  33. 33.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹61 (c) ₹15 (d) ₹60
  34. 34.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 12 days
  35. 35.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
  36. 36.If 4 mangoes cost ₹44, how much do 7 mangoes cost? (a) ₹308 (b) ₹47 (c) ₹88 (d) ₹77
  37. 37.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 17 days (d) 13 days
  38. 38.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 11 days (d) 16 days
  39. 39.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 12 days (d) 7 days
  40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 3 days (d) 2 days

Answer key

  1. ₹198
  2. 6 days
  3. ₹60
  4. ₹81
  5. ₹48
  6. 8 days
  7. 20 days
  8. 3 days
  9. ₹333
  10. ₹90
  11. ₹48
  12. ₹120
  13. ₹140
  14. 3 days
  15. 7 days
  16. ₹400
  17. 21 days
  18. ₹34
  19. ₹128
  20. ₹30
  21. ₹160
  22. 7 days
  23. 7 days
  24. 15 days
  25. 12 days
  26. 28 days
  27. ₹66
  28. ₹306
  29. 40 days
  30. ₹84
  31. 39 days
  32. ₹172
  33. ₹60
  34. 4 days
  35. 25 days
  36. ₹77
  37. 10 days
  38. 9 days
  39. 12 days
  40. 3 days

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