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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 389 · 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 7 pens cost ₹70, how much do 2 pens cost? (a) ₹65 (b) ₹20 (c) ₹140 (d) ₹30
  2. 2.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹110 (b) ₹154 (c) ₹66 (d) ₹22
  3. 3.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
  4. 4.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 4 days (d) 5 days
  5. 5.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹160 (b) ₹144 (c) ₹80 (d) ₹16
  6. 6.If 7 notebooks cost ₹98, how much do 2 notebooks cost? (a) ₹196 (b) ₹28 (c) ₹42 (d) ₹93
  7. 7.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹147 (b) ₹168 (c) ₹84 (d) ₹21
  8. 8.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹304 (b) ₹38 (c) ₹266 (d) ₹152
  9. 9.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 12 days (c) 8 days (d) 5 days
  10. 10.If 5 kites cost ₹75, how much do 6 kites cost? (a) ₹76 (b) ₹90 (c) ₹450 (d) ₹105
  11. 11.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 19 days (d) 18 days
  12. 12.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹52 (b) ₹78 (c) ₹65 (d) ₹13
  13. 13.If 9 kites cost ₹36, how much do 12 kites cost? (a) ₹48 (b) ₹52 (c) ₹39 (d) ₹432
  14. 14.If 6 kites cost ₹84, how much do 5 kites cost? (a) ₹70 (b) ₹420 (c) ₹83 (d) ₹84
  15. 15.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹273 (b) ₹195 (c) ₹39 (d) ₹351
  16. 16.If 8 pens cost ₹96, how much do 4 pens cost? (a) ₹60 (b) ₹48 (c) ₹384 (d) ₹92
  17. 17.₹352 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹288 (b) ₹32 (c) ₹176 (d) ₹64
  18. 18.If 6 mangoes cost ₹54, how much do 3 mangoes cost? (a) ₹27 (b) ₹51 (c) ₹162 (d) ₹36
  19. 19.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹51 (d) ₹85
  20. 20.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 45 days (d) 5 days
  21. 21.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹28 (b) ₹63 (c) ₹70 (d) ₹7
  22. 22.If 7 kites cost ₹28, how much do 5 kites cost? (a) ₹20 (b) ₹24 (c) ₹26 (d) ₹140
  23. 23.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹72 (b) ₹84 (c) ₹12 (d) ₹42
  24. 24.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 8 days (d) 9 days
  25. 25.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹136 (d) ₹119
  26. 26.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹49 (c) ₹7 (d) ₹35
  27. 27.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹344 (c) ₹345 (d) ₹43
  28. 28.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹25 (c) ₹5 (d) ₹45
  29. 29.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 17 days (d) 7 days
  30. 30.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 31 days (d) 30 days
  31. 31.If 5 kites cost ₹55, how much do 3 kites cost? (a) ₹165 (b) ₹53 (c) ₹44 (d) ₹33
  32. 32.If 3 kites cost ₹60, how much do 7 kites cost? (a) ₹64 (b) ₹140 (c) ₹420 (d) ₹160
  33. 33.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 27 days (d) 3 days
  34. 34.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 11 days
  35. 35.If 8 notebooks cost ₹136, how much do 9 notebooks cost? (a) ₹170 (b) ₹137 (c) ₹1224 (d) ₹153
  36. 36.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹165 (c) ₹30 (d) ₹180
  37. 37.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 17 days (d) 10 days
  38. 38.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 5 days (d) 16 days
  39. 39.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹78 (d) ₹104
  40. 40.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹288 (b) ₹108 (c) ₹36 (d) ₹198

Answer key

  1. ₹20
  2. ₹154
  3. 3 days
  4. 6 days
  5. ₹144
  6. ₹28
  7. ₹147
  8. ₹266
  9. 20 days
  10. ₹90
  11. 18 days
  12. ₹65
  13. ₹48
  14. ₹70
  15. ₹351
  16. ₹48
  17. ₹288
  18. ₹27
  19. ₹85
  20. 45 days
  21. ₹63
  22. ₹20
  23. ₹72
  24. 4 days
  25. ₹119
  26. ₹42
  27. ₹344
  28. ₹45
  29. 32 days
  30. 30 days
  31. ₹33
  32. ₹140
  33. 3 days
  34. 15 days
  35. ₹153
  36. ₹180
  37. 16 days
  38. 4 days
  39. ₹78
  40. ₹288

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