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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 282 · 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. 1.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
  2. 2.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
  3. 3.If 2 mangoes cost ₹10, how much do 9 mangoes cost? (a) ₹45 (b) ₹17 (c) ₹90 (d) ₹50
  4. 4.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹136 (b) ₹51 (c) ₹153 (d) ₹17
  5. 5.If 2 mangoes cost ₹50, how much do 3 mangoes cost? (a) ₹100 (b) ₹150 (c) ₹75 (d) ₹51
  6. 6.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 11 days (d) 45 days
  7. 7.If 5 notebooks cost ₹100, how much do 8 notebooks cost? (a) ₹103 (b) ₹800 (c) ₹160 (d) ₹180
  8. 8.If 8 kites cost ₹104, how much do 11 kites cost? (a) ₹107 (b) ₹156 (c) ₹143 (d) ₹1144
  9. 9.If 5 pens cost ₹75, how much do 6 pens cost? (a) ₹450 (b) ₹76 (c) ₹105 (d) ₹90
  10. 10.If 3 mangoes cost ₹18, how much do 10 mangoes cost? (a) ₹66 (b) ₹25 (c) ₹60 (d) ₹180
  11. 11.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 3 days (d) 4 days
  12. 12.If 6 notebooks cost ₹108, how much do 3 notebooks cost? (a) ₹105 (b) ₹324 (c) ₹72 (d) ₹54
  13. 13.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 12 days (d) 11 days
  14. 14.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 10 days
  15. 15.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹35 (b) ₹58 (c) ₹28 (d) ₹252
  16. 16.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹180 (b) ₹80 (c) ₹20 (d) ₹130
  17. 17.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 12 days (d) 23 days
  18. 18.If 3 pens cost ₹33, how much do 4 pens cost? (a) ₹44 (b) ₹34 (c) ₹132 (d) ₹55
  19. 19.If 4 notebooks cost ₹52, how much do 9 notebooks cost? (a) ₹468 (b) ₹57 (c) ₹130 (d) ₹117
  20. 20.If 9 mangoes cost ₹108, how much do 3 mangoes cost? (a) ₹324 (b) ₹36 (c) ₹48 (d) ₹102
  21. 21.If 9 pens cost ₹99, how much do 6 pens cost? (a) ₹594 (b) ₹77 (c) ₹66 (d) ₹96
  22. 22.If 5 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹210 (b) ₹42 (c) ₹102 (d) ₹63
  23. 23.If 4 pens cost ₹88, how much do 2 pens cost? (a) ₹176 (b) ₹66 (c) ₹44 (d) ₹86
  24. 24.If 6 mangoes cost ₹138, how much do 7 mangoes cost? (a) ₹966 (b) ₹184 (c) ₹161 (d) ₹139
  25. 25.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 19 days (c) 11 days (d) 35 days
  26. 26.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 14 days (d) 6 days
  27. 27.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 7 days (d) 3 days
  28. 28.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹42 (b) ₹336 (c) ₹273 (d) ₹210
  29. 29.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹132 (d) ₹192
  30. 30.If 6 pens cost ₹78, how much do 2 pens cost? (a) ₹26 (b) ₹74 (c) ₹156 (d) ₹39
  31. 31.If 4 kites cost ₹64, how much do 6 kites cost? (a) ₹96 (b) ₹112 (c) ₹66 (d) ₹384
  32. 32.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 17 days (d) 13 days
  33. 33.If 7 pens cost ₹119, how much do 3 pens cost? (a) ₹357 (b) ₹115 (c) ₹68 (d) ₹51
  34. 34.If 2 notebooks cost ₹38, how much do 12 notebooks cost? (a) ₹456 (b) ₹48 (c) ₹228 (d) ₹247
  35. 35.If 6 mangoes cost ₹114, how much do 3 mangoes cost? (a) ₹76 (b) ₹342 (c) ₹111 (d) ₹57
  36. 36.If 7 pens cost ₹147, how much do 12 pens cost? (a) ₹152 (b) ₹1764 (c) ₹273 (d) ₹252
  37. 37.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
  38. 38.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 18 days (d) 36 days
  39. 39.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹204 (b) ₹102 (c) ₹34 (d) ₹170
  40. 40.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 60 days (c) 9 days (d) 61 days

Answer key

  1. 26 days
  2. 45 days
  3. ₹45
  4. ₹136
  5. ₹75
  6. 45 days
  7. ₹160
  8. ₹143
  9. ₹90
  10. ₹60
  11. 3 days
  12. ₹54
  13. 12 days
  14. 12 days
  15. ₹28
  16. ₹180
  17. 24 days
  18. ₹44
  19. ₹117
  20. ₹36
  21. ₹66
  22. ₹42
  23. ₹44
  24. ₹161
  25. 35 days
  26. 6 days
  27. 3 days
  28. ₹336
  29. ₹192
  30. ₹26
  31. ₹96
  32. 16 days
  33. ₹51
  34. ₹228
  35. ₹57
  36. ₹252
  37. 16 days
  38. 36 days
  39. ₹170
  40. 60 days

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