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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 470 · 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) ₹120 (b) ₹168 (c) ₹216 (d) ₹24
  2. 2.₹95 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹76 (b) ₹57 (c) ₹19 (d) ₹38
  3. 3.If 6 pens cost ₹60, how much do 4 pens cost? (a) ₹58 (b) ₹40 (c) ₹50 (d) ₹240
  4. 4.If 4 kites cost ₹12, how much do 12 kites cost? (a) ₹39 (b) ₹20 (c) ₹36 (d) ₹144
  5. 5.If 3 mangoes cost ₹57, how much do 10 mangoes cost? (a) ₹570 (b) ₹64 (c) ₹190 (d) ₹209
  6. 6.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹84 (b) ₹21 (c) ₹168 (d) ₹147
  7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 27 days (c) 26 days (d) 28 days
  8. 8.If 6 mangoes cost ₹150, how much do 4 mangoes cost? (a) ₹100 (b) ₹148 (c) ₹125 (d) ₹600
  9. 9.If 8 notebooks cost ₹72, how much do 3 notebooks cost? (a) ₹67 (b) ₹36 (c) ₹216 (d) ₹27
  10. 10.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 9 days (c) 8 days (d) 15 days
  11. 11.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹49 (b) ₹196 (c) ₹98 (d) ₹147
  12. 12.If 8 kites cost ₹56, how much do 2 kites cost? (a) ₹21 (b) ₹112 (c) ₹14 (d) ₹50
  13. 13.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹224 (b) ₹32 (c) ₹192 (d) ₹160
  14. 14.If 8 notebooks cost ₹128, how much do 2 notebooks cost? (a) ₹32 (b) ₹122 (c) ₹256 (d) ₹48
  15. 15.If 6 pens cost ₹144, how much do 5 pens cost? (a) ₹720 (b) ₹120 (c) ₹143 (d) ₹144
  16. 16.If 9 pens cost ₹126, how much do 2 pens cost? (a) ₹28 (b) ₹119 (c) ₹252 (d) ₹42
  17. 17.If 3 notebooks cost ₹36, how much do 6 notebooks cost? (a) ₹72 (b) ₹39 (c) ₹216 (d) ₹84
  18. 18.If 4 kites cost ₹72, how much do 5 kites cost? (a) ₹90 (b) ₹108 (c) ₹360 (d) ₹73
  19. 19.If 4 kites cost ₹100, how much do 11 kites cost? (a) ₹1100 (b) ₹107 (c) ₹300 (d) ₹275
  20. 20.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹148 (b) ₹259 (c) ₹296 (d) ₹37
  21. 21.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 8 days (d) 7 days
  22. 22.If 8 notebooks cost ₹112, how much do 2 notebooks cost? (a) ₹42 (b) ₹106 (c) ₹28 (d) ₹224
  23. 23.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 41 days (c) 16 days (d) 40 days
  24. 24.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 18 days (d) 28 days
  25. 25.If 7 mangoes cost ₹35, how much do 9 mangoes cost? (a) ₹37 (b) ₹315 (c) ₹45 (d) ₹50
  26. 26.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹110 (b) ₹44 (c) ₹99 (d) ₹11
  27. 27.If 4 notebooks cost ₹80, how much do 2 notebooks cost? (a) ₹60 (b) ₹160 (c) ₹40 (d) ₹78
  28. 28.₹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
  29. 29.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
  30. 30.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹48 (c) ₹24 (d) ₹72
  31. 31.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹10 (b) ₹50 (c) ₹55 (d) ₹60
  32. 32.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 48 days (c) 21 days (d) 3 days
  33. 33.If 4 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹35 (b) ₹64 (c) ₹56 (d) ₹224
  34. 34.If 3 pens cost ₹69, how much do 4 pens cost? (a) ₹70 (b) ₹115 (c) ₹276 (d) ₹92
  35. 35.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 27 days (d) 13 days
  36. 36.₹224 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹112 (b) ₹84 (c) ₹28 (d) ₹140
  37. 37.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹210 (b) ₹175 (c) ₹35 (d) ₹70
  38. 38.If 3 kites cost ₹15, how much do 7 kites cost? (a) ₹19 (b) ₹105 (c) ₹40 (d) ₹35
  39. 39.₹451 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹287 (b) ₹41 (c) ₹205 (d) ₹246
  40. 40.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹144 (b) ₹80 (c) ₹112 (d) ₹16

Answer key

  1. ₹216
  2. ₹57
  3. ₹40
  4. ₹36
  5. ₹190
  6. ₹147
  7. 27 days
  8. ₹100
  9. ₹27
  10. 8 days
  11. ₹147
  12. ₹14
  13. ₹224
  14. ₹32
  15. ₹120
  16. ₹28
  17. ₹72
  18. ₹90
  19. ₹275
  20. ₹259
  21. 7 days
  22. ₹28
  23. 40 days
  24. 7 days
  25. ₹45
  26. ₹99
  27. ₹40
  28. ₹48
  29. 5 days
  30. ₹48
  31. ₹60
  32. 3 days
  33. ₹56
  34. ₹92
  35. 27 days
  36. ₹140
  37. ₹175
  38. ₹35
  39. ₹246
  40. ₹144

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