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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 887 · 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.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹154 (b) ₹176 (c) ₹132 (d) ₹44
  2. 2.If 4 kites cost ₹92, how much do 10 kites cost? (a) ₹98 (b) ₹230 (c) ₹253 (d) ₹920
  3. 3.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹84 (b) ₹64 (c) ₹252 (d) ₹105
  4. 4.If 9 pens cost ₹36, how much do 8 pens cost? (a) ₹32 (b) ₹35 (c) ₹36 (d) ₹288
  5. 5.₹451 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹123 (d) ₹369
  6. 6.If 8 kites cost ₹200, how much do 7 kites cost? (a) ₹199 (b) ₹200 (c) ₹1400 (d) ₹175
  7. 7.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 11 days (d) 10 days
  8. 8.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹36 (b) ₹324 (c) ₹144 (d) ₹234
  9. 9.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹44 (d) ₹22
  10. 10.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹100 (b) ₹300 (c) ₹125 (d) ₹76
  11. 11.If 5 kites cost ₹15, how much do 2 kites cost? (a) ₹12 (b) ₹30 (c) ₹9 (d) ₹6
  12. 12.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 28 days (d) 15 days
  13. 13.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹64 (c) ₹8 (d) ₹52
  14. 14.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹60 (d) ₹40
  15. 15.If 8 notebooks cost ₹104, how much do 11 notebooks cost? (a) ₹143 (b) ₹1144 (c) ₹156 (d) ₹107
  16. 16.If 4 pens cost ₹28, how much do 6 pens cost? (a) ₹30 (b) ₹42 (c) ₹49 (d) ₹168
  17. 17.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹88 (b) ₹132 (c) ₹66 (d) ₹44
  18. 18.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹48 (d) ₹64
  19. 19.If 7 pens cost ₹105, how much do 2 pens cost? (a) ₹30 (b) ₹45 (c) ₹210 (d) ₹100
  20. 20.If 3 pens cost ₹27, how much do 7 pens cost? (a) ₹31 (b) ₹189 (c) ₹63 (d) ₹72
  21. 21.If 4 mangoes cost ₹84, how much do 11 mangoes cost? (a) ₹252 (b) ₹91 (c) ₹231 (d) ₹924
  22. 22.₹171 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹152 (b) ₹153 (c) ₹19 (d) ₹171
  23. 23.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 1 day (c) 8 days (d) 7 days
  24. 24.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 37 days (c) 15 days (d) 36 days
  25. 25.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 14 days (d) 19 days
  26. 26.If 6 kites cost ₹144, how much do 11 kites cost? (a) ₹264 (b) ₹1584 (c) ₹149 (d) ₹288
  27. 27.If 3 kites cost ₹21, how much do 5 kites cost? (a) ₹23 (b) ₹105 (c) ₹42 (d) ₹35
  28. 28.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹84 (b) ₹24 (c) ₹72 (d) ₹96
  29. 29.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 7 days (d) 17 days
  30. 30.If 8 mangoes cost ₹136, how much do 5 mangoes cost? (a) ₹102 (b) ₹680 (c) ₹85 (d) ₹133
  31. 31.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 12 days
  32. 32.6 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
  33. 33.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 9 days (d) 13 days
  34. 34.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 17 days (d) 5 days
  35. 35.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹33 (b) ₹297 (c) ₹264 (d) ₹165
  36. 36.If 5 mangoes cost ₹115, how much do 6 mangoes cost? (a) ₹690 (b) ₹161 (c) ₹116 (d) ₹138
  37. 37.3 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) 2 days (d) 13 days
  38. 38.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹351 (d) ₹390
  39. 39.If 5 mangoes cost ₹70, how much do 3 mangoes cost? (a) ₹68 (b) ₹56 (c) ₹42 (d) ₹210
  40. 40.If 7 pens cost ₹21, how much do 2 pens cost? (a) ₹6 (b) ₹16 (c) ₹42 (d) ₹9

Answer key

  1. ₹176
  2. ₹230
  3. ₹84
  4. ₹32
  5. ₹328
  6. ₹175
  7. 10 days
  8. ₹324
  9. ₹66
  10. ₹100
  11. ₹6
  12. 27 days
  13. ₹64
  14. ₹60
  15. ₹143
  16. ₹42
  17. ₹88
  18. ₹48
  19. ₹30
  20. ₹63
  21. ₹231
  22. ₹152
  23. 7 days
  24. 36 days
  25. 18 days
  26. ₹264
  27. ₹35
  28. ₹96
  29. 7 days
  30. ₹85
  31. 6 days
  32. 27 days
  33. 25 days
  34. 5 days
  35. ₹264
  36. ₹138
  37. 1 day
  38. ₹351
  39. ₹42
  40. ₹6

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