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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 253 · 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. 1.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 21 days (d) 20 days
  2. 2.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 5 days (d) 4 days
  3. 3.If 2 pens cost ₹18, how much do 8 pens cost? (a) ₹24 (b) ₹144 (c) ₹72 (d) ₹81
  4. 4.₹247 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹19 (b) ₹190 (c) ₹171 (d) ₹76
  5. 5.If 5 kites cost ₹70, how much do 4 kites cost? (a) ₹280 (b) ₹56 (c) ₹70 (d) ₹69
  6. 6.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹51 (b) ₹153 (c) ₹17 (d) ₹136
  7. 7.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹256 (c) ₹32 (d) ₹208
  8. 8.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹175 (d) ₹250
  9. 9.₹539 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹343 (b) ₹49 (c) ₹245 (d) ₹294
  10. 10.If 9 kites cost ₹90, how much do 5 kites cost? (a) ₹86 (b) ₹450 (c) ₹50 (d) ₹60
  11. 11.If 8 pens cost ₹192, how much do 9 pens cost? (a) ₹193 (b) ₹1728 (c) ₹240 (d) ₹216
  12. 12.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹39 (b) ₹312 (c) ₹195 (d) ₹351
  13. 13.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹198 (b) ₹231 (c) ₹165 (d) ₹33
  14. 14.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹88 (c) ₹11 (d) ₹77
  15. 15.₹363 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹264 (b) ₹33 (c) ₹297 (d) ₹99
  16. 16.If 5 pens cost ₹30, how much do 6 pens cost? (a) ₹180 (b) ₹31 (c) ₹42 (d) ₹36
  17. 17.If 6 kites cost ₹138, how much do 3 kites cost? (a) ₹135 (b) ₹92 (c) ₹69 (d) ₹414
  18. 18.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹35 (d) ₹42
  19. 19.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹360 (b) ₹200 (c) ₹40 (d) ₹400
  20. 20.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹215 (d) ₹301
  21. 21.If 6 kites cost ₹126, how much do 2 kites cost? (a) ₹252 (b) ₹42 (c) ₹122 (d) ₹63
  22. 22.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
  23. 23.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹28 (b) ₹8 (c) ₹24 (d) ₹32
  24. 24.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹133 (c) ₹171 (d) ₹19
  25. 25.If 4 pens cost ₹12, how much do 2 pens cost? (a) ₹6 (b) ₹10 (c) ₹24 (d) ₹9
  26. 26.If 9 mangoes cost ₹63, how much do 3 mangoes cost? (a) ₹28 (b) ₹189 (c) ₹57 (d) ₹21
  27. 27.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹110 (b) ₹80 (c) ₹140 (d) ₹20
  28. 28.If 7 mangoes cost ₹49, how much do 10 mangoes cost? (a) ₹70 (b) ₹77 (c) ₹52 (d) ₹490
  29. 29.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹242 (b) ₹220 (c) ₹44 (d) ₹264
  30. 30.If 4 kites cost ₹64, how much do 3 kites cost? (a) ₹63 (b) ₹192 (c) ₹64 (d) ₹48
  31. 31.₹161 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹92 (d) ₹115
  32. 32.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹60 (d) ₹45
  33. 33.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 34 days (d) 33 days
  34. 34.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹154 (b) ₹22 (c) ₹176 (d) ₹88
  35. 35.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 8 days (d) 7 days
  36. 36.If 9 pens cost ₹27, how much do 2 pens cost? (a) ₹6 (b) ₹20 (c) ₹54 (d) ₹9
  37. 37.If 2 notebooks cost ₹14, how much do 12 notebooks cost? (a) ₹24 (b) ₹168 (c) ₹91 (d) ₹84
  38. 38.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 2 days (b) 12 days (c) 18 days (d) 3 days
  39. 39.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 17 days (d) 22 days
  40. 40.If 8 kites cost ₹88, how much do 5 kites cost? (a) ₹85 (b) ₹55 (c) ₹440 (d) ₹66

Answer key

  1. 20 days
  2. 9 days
  3. ₹72
  4. ₹171
  5. ₹56
  6. ₹136
  7. ₹256
  8. ₹250
  9. ₹294
  10. ₹50
  11. ₹216
  12. ₹312
  13. ₹231
  14. ₹77
  15. ₹264
  16. ₹36
  17. ₹69
  18. ₹35
  19. ₹360
  20. ₹301
  21. ₹42
  22. 45 days
  23. ₹32
  24. ₹171
  25. ₹6
  26. ₹21
  27. ₹140
  28. ₹70
  29. ₹264
  30. ₹48
  31. ₹92
  32. ₹60
  33. 33 days
  34. ₹154
  35. 7 days
  36. ₹6
  37. ₹84
  38. 2 days
  39. 21 days
  40. ₹55

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