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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 382 · 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 5 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹60 (b) ₹12 (c) ₹14 (d) ₹15
  2. 2.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹390 (b) ₹351 (c) ₹39 (d) ₹78
  3. 3.If 7 kites cost ₹98, how much do 9 kites cost? (a) ₹140 (b) ₹882 (c) ₹100 (d) ₹126
  4. 4.If 7 notebooks cost ₹168, how much do 12 notebooks cost? (a) ₹288 (b) ₹173 (c) ₹2016 (d) ₹312
  5. 5.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹171 (b) ₹19 (c) ₹95 (d) ₹152
  6. 6.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 2 days (c) 3 days (d) 4 days
  7. 7.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
  8. 8.₹45 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹35 (b) ₹5 (c) ₹10 (d) ₹40
  9. 9.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹75 (d) ₹125
  10. 10.If 8 kites cost ₹80, how much do 12 kites cost? (a) ₹130 (b) ₹120 (c) ₹960 (d) ₹84
  11. 11.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 33 days (c) 2 days (d) 32 days
  12. 12.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 19 days
  13. 13.If 2 mangoes cost ₹30, how much do 5 mangoes cost? (a) ₹150 (b) ₹90 (c) ₹33 (d) ₹75
  14. 14.If 4 kites cost ₹76, how much do 7 kites cost? (a) ₹532 (b) ₹152 (c) ₹79 (d) ₹133
  15. 15.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 13 days (d) 3 days
  16. 16.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹308 (c) ₹352 (d) ₹176
  17. 17.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹99 (b) ₹18 (c) ₹162 (d) ₹36
  18. 18.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹16 (c) ₹96 (d) ₹80
  19. 19.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
  20. 20.If 8 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹54 (b) ₹49 (c) ₹432 (d) ₹60
  21. 21.If 9 notebooks cost ₹180, how much do 5 notebooks cost? (a) ₹900 (b) ₹176 (c) ₹100 (d) ₹120
  22. 22.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹140 (b) ₹14 (c) ₹70 (d) ₹126
  23. 23.If 9 kites cost ₹108, how much do 10 kites cost? (a) ₹132 (b) ₹120 (c) ₹1080 (d) ₹109
  24. 24.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 24 days (c) 7 days (d) 17 days
  25. 25.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹6 (b) ₹48 (c) ₹30 (d) ₹39
  26. 26.If 3 kites cost ₹33, how much do 12 kites cost? (a) ₹42 (b) ₹396 (c) ₹143 (d) ₹132
  27. 27.If 8 pens cost ₹104, how much do 6 pens cost? (a) ₹78 (b) ₹102 (c) ₹91 (d) ₹624
  28. 28.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 9 days (c) 39 days (d) 17 days
  29. 29.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹17 (b) ₹119 (c) ₹85 (d) ₹153
  30. 30.₹242 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹121 (b) ₹22 (c) ₹154 (d) ₹88
  31. 31.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 17 days (d) 11 days
  32. 32.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 28 days (d) 26 days
  33. 33.If 3 mangoes cost ₹66, how much do 2 mangoes cost? (a) ₹44 (b) ₹132 (c) ₹65 (d) ₹66
  34. 34.₹108 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹84 (b) ₹24 (c) ₹54 (d) ₹12
  35. 35.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹76 (d) ₹77
  36. 36.If 2 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹50 (b) ₹480 (c) ₹240 (d) ₹260
  37. 37.If 6 kites cost ₹138, how much do 5 kites cost? (a) ₹690 (b) ₹115 (c) ₹138 (d) ₹137
  38. 38.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹36 (c) ₹24 (d) ₹12
  39. 39.If 3 mangoes cost ₹33, how much do 8 mangoes cost? (a) ₹99 (b) ₹38 (c) ₹264 (d) ₹88
  40. 40.If 9 kites cost ₹72, how much do 3 kites cost? (a) ₹66 (b) ₹32 (c) ₹216 (d) ₹24

Answer key

  1. ₹12
  2. ₹351
  3. ₹126
  4. ₹288
  5. ₹152
  6. 3 days
  7. 7 days
  8. ₹35
  9. ₹100
  10. ₹120
  11. 32 days
  12. 35 days
  13. ₹75
  14. ₹133
  15. 12 days
  16. ₹308
  17. ₹162
  18. ₹80
  19. 9 days
  20. ₹54
  21. ₹100
  22. ₹126
  23. ₹120
  24. 6 days
  25. ₹48
  26. ₹132
  27. ₹78
  28. 39 days
  29. ₹153
  30. ₹154
  31. 35 days
  32. 27 days
  33. ₹44
  34. ₹84
  35. ₹76
  36. ₹240
  37. ₹115
  38. ₹36
  39. ₹88
  40. ₹24

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