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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 862 · 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.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹24 (b) ₹216 (c) ₹168 (d) ₹120
  2. 2.If 6 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹44 (b) ₹40 (c) ₹28 (d) ₹240
  3. 3.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
  4. 4.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹82 (b) ₹83 (c) ₹123 (d) ₹41
  5. 5.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 4 days (d) 16 days
  6. 6.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹45 (c) ₹25 (d) ₹5
  7. 7.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹296 (b) ₹333 (c) ₹111 (d) ₹37
  8. 8.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 11 days (d) 3 days
  9. 9.If 4 kites cost ₹40, how much do 12 kites cost? (a) ₹130 (b) ₹480 (c) ₹120 (d) ₹48
  10. 10.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 3 days (d) 4 days
  11. 11.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹128 (b) ₹144 (c) ₹32 (d) ₹160
  12. 12.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹66 (d) ₹121
  13. 13.If 2 pens cost ₹14, how much do 5 pens cost? (a) ₹70 (b) ₹17 (c) ₹42 (d) ₹35
  14. 14.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹160 (b) ₹176 (c) ₹192 (d) ₹32
  15. 15.If 3 pens cost ₹33, how much do 12 pens cost? (a) ₹143 (b) ₹42 (c) ₹396 (d) ₹132
  16. 16.₹259 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹74 (b) ₹185 (c) ₹37 (d) ₹222
  17. 17.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹90 (b) ₹105 (c) ₹75 (d) ₹15
  18. 18.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 11 days (d) 13 days
  19. 19.If 3 kites cost ₹57, how much do 4 kites cost? (a) ₹76 (b) ₹228 (c) ₹95 (d) ₹58
  20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
  21. 21.If 4 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹126 (b) ₹60 (c) ₹448 (d) ₹112
  22. 22.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
  23. 23.If 7 notebooks cost ₹84, how much do 10 notebooks cost? (a) ₹132 (b) ₹840 (c) ₹120 (d) ₹87
  24. 24.If 5 notebooks cost ₹50, how much do 9 notebooks cost? (a) ₹100 (b) ₹54 (c) ₹90 (d) ₹450
  25. 25.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹5 (d) ₹40
  26. 26.If 2 mangoes cost ₹48, how much do 8 mangoes cost? (a) ₹384 (b) ₹216 (c) ₹192 (d) ₹54
  27. 27.If 9 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹540 (b) ₹60 (c) ₹66 (d) ₹55
  28. 28.If 4 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹42 (b) ₹29 (c) ₹140 (d) ₹35
  29. 29.If 7 kites cost ₹98, how much do 6 kites cost? (a) ₹97 (b) ₹588 (c) ₹98 (d) ₹84
  30. 30.If 3 notebooks cost ₹36, how much do 6 notebooks cost? (a) ₹84 (b) ₹39 (c) ₹72 (d) ₹216
  31. 31.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 7 days (d) 10 days
  32. 32.If 9 kites cost ₹45, how much do 5 kites cost? (a) ₹30 (b) ₹41 (c) ₹225 (d) ₹25
  33. 33.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 5 days
  34. 34.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹250 (b) ₹225 (c) ₹25 (d) ₹100
  35. 35.If 3 notebooks cost ₹69, how much do 10 notebooks cost? (a) ₹76 (b) ₹253 (c) ₹690 (d) ₹230
  36. 36.If 9 notebooks cost ₹27, how much do 10 notebooks cost? (a) ₹270 (b) ₹28 (c) ₹33 (d) ₹30
  37. 37.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 17 days (c) 16 days (d) 4 days
  38. 38.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 12 days (d) 2 days
  39. 39.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 1 day (d) 2 days
  40. 40.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 10 days (d) 18 days

Answer key

  1. ₹216
  2. ₹40
  3. 25 days
  4. ₹82
  5. 4 days
  6. ₹45
  7. ₹296
  8. 10 days
  9. ₹120
  10. 3 days
  11. ₹160
  12. ₹176
  13. ₹35
  14. ₹192
  15. ₹132
  16. ₹185
  17. ₹90
  18. 10 days
  19. ₹76
  20. 7 days
  21. ₹112
  22. 4 days
  23. ₹120
  24. ₹90
  25. ₹40
  26. ₹192
  27. ₹60
  28. ₹35
  29. ₹84
  30. ₹72
  31. 10 days
  32. ₹25
  33. 5 days
  34. ₹225
  35. ₹230
  36. ₹30
  37. 16 days
  38. 3 days
  39. 8 days
  40. 42 days

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