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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 897 · 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. 1.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 16 days
  2. 2.If 4 mangoes cost ₹48, how much do 6 mangoes cost? (a) ₹288 (b) ₹50 (c) ₹72 (d) ₹84
  3. 3.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹34 (d) ₹17
  4. 4.₹264 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹132 (b) ₹110 (c) ₹154 (d) ₹22
  5. 5.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹63 (b) ₹70 (c) ₹56 (d) ₹14
  6. 6.If 8 kites cost ₹72, how much do 4 kites cost? (a) ₹68 (b) ₹288 (c) ₹45 (d) ₹36
  7. 7.If 7 pens cost ₹28, how much do 2 pens cost? (a) ₹56 (b) ₹8 (c) ₹12 (d) ₹23
  8. 8.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 10 days (c) 20 days (d) 14 days
  9. 9.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹44 (d) ₹33
  10. 10.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 57 days (c) 20 days (d) 56 days
  11. 11.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹162 (c) ₹18 (d) ₹72
  12. 12.If 2 kites cost ₹36, how much do 3 kites cost? (a) ₹108 (b) ₹37 (c) ₹54 (d) ₹72
  13. 13.If 6 kites cost ₹102, how much do 3 kites cost? (a) ₹68 (b) ₹51 (c) ₹99 (d) ₹306
  14. 14.If 6 notebooks cost ₹78, how much do 2 notebooks cost? (a) ₹39 (b) ₹74 (c) ₹156 (d) ₹26
  15. 15.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹245 (b) ₹175 (c) ₹35 (d) ₹210
  16. 16.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 16 days (c) 29 days (d) 8 days
  17. 17.If 6 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹42 (b) ₹63 (c) ₹252 (d) ₹122
  18. 18.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 19 days (d) 11 days
  19. 19.If 2 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹23 (b) ₹72 (c) ₹126 (d) ₹63
  20. 20.If 2 notebooks cost ₹40, how much do 5 notebooks cost? (a) ₹100 (b) ₹43 (c) ₹200 (d) ₹120
  21. 21.If 5 pens cost ₹15, how much do 6 pens cost? (a) ₹16 (b) ₹21 (c) ₹90 (d) ₹18
  22. 22.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹11 (b) ₹88 (c) ₹99 (d) ₹33
  23. 23.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
  24. 24.If 4 kites cost ₹96, how much do 10 kites cost? (a) ₹240 (b) ₹102 (c) ₹264 (d) ₹960
  25. 25.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 18 days (c) 30 days (d) 12 days
  26. 26.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 9 days
  27. 27.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹88 (b) ₹44 (c) ₹132 (d) ₹176
  28. 28.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹65 (d) ₹52
  29. 29.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 15 days (d) 14 days
  30. 30.If 7 notebooks cost ₹35, how much do 9 notebooks cost? (a) ₹37 (b) ₹50 (c) ₹45 (d) ₹315
  31. 31.If 3 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹90 (b) ₹105 (c) ₹270 (d) ₹48
  32. 32.If 6 kites cost ₹60, how much do 3 kites cost? (a) ₹30 (b) ₹180 (c) ₹40 (d) ₹57
  33. 33.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  34. 34.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹46 (b) ₹69 (c) ₹23 (d) ₹92
  35. 35.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹360 (d) ₹280
  36. 36.If 2 kites cost ₹50, how much do 6 kites cost? (a) ₹300 (b) ₹54 (c) ₹150 (d) ₹175
  37. 37.If 2 notebooks cost ₹10, how much do 11 notebooks cost? (a) ₹55 (b) ₹60 (c) ₹19 (d) ₹110
  38. 38.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹390 (d) ₹351
  39. 39.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹329 (b) ₹328 (c) ₹41 (d) ₹369
  40. 40.If 8 mangoes cost ₹192, how much do 6 mangoes cost? (a) ₹190 (b) ₹168 (c) ₹144 (d) ₹1152

Answer key

  1. 15 days
  2. ₹72
  3. ₹119
  4. ₹154
  5. ₹70
  6. ₹36
  7. ₹8
  8. 20 days
  9. ₹33
  10. 56 days
  11. ₹162
  12. ₹54
  13. ₹51
  14. ₹26
  15. ₹245
  16. 28 days
  17. ₹42
  18. 18 days
  19. ₹63
  20. ₹100
  21. ₹18
  22. ₹88
  23. 5 days
  24. ₹240
  25. 30 days
  26. 8 days
  27. ₹132
  28. ₹65
  29. 14 days
  30. ₹45
  31. ₹90
  32. ₹30
  33. 9 days
  34. ₹69
  35. ₹360
  36. ₹150
  37. ₹55
  38. ₹351
  39. ₹328
  40. ₹144

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