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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 297 · 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.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹185 (b) ₹37 (c) ₹333 (d) ₹259
  2. 2.₹90 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹10 (c) ₹50 (d) ₹40
  3. 3.₹144 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹126 (b) ₹72 (c) ₹144 (d) ₹18
  4. 4.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 18 days (c) 4 days (d) 6 days
  5. 5.If 4 mangoes cost ₹12, how much do 11 mangoes cost? (a) ₹36 (b) ₹33 (c) ₹132 (d) ₹19
  6. 6.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 17 days (d) 21 days
  7. 7.If 7 pens cost ₹28, how much do 2 pens cost? (a) ₹56 (b) ₹23 (c) ₹8 (d) ₹12
  8. 8.If 5 mangoes cost ₹70, how much do 10 mangoes cost? (a) ₹154 (b) ₹140 (c) ₹75 (d) ₹700
  9. 9.If 4 kites cost ₹84, how much do 2 kites cost? (a) ₹82 (b) ₹42 (c) ₹63 (d) ₹168
  10. 10.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹102 (d) ₹119
  11. 11.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹114 (b) ₹95 (c) ₹38 (d) ₹76
  12. 12.7 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
  13. 13.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹80 (d) ₹16
  14. 14.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 24 days (c) 6 days (d) 8 days
  15. 15.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹37 (b) ₹48 (c) ₹252 (d) ₹42
  16. 16.If 4 pens cost ₹88, how much do 8 pens cost? (a) ₹92 (b) ₹176 (c) ₹198 (d) ₹704
  17. 17.₹315 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹35 (b) ₹280 (c) ₹70 (d) ₹245
  18. 18.If 8 notebooks cost ₹48, how much do 4 notebooks cost? (a) ₹30 (b) ₹192 (c) ₹24 (d) ₹44
  19. 19.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 4 days (d) 6 days
  20. 20.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 8 days (d) 9 days
  21. 21.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹203 (b) ₹174 (c) ₹29 (d) ₹145
  22. 22.If 4 kites cost ₹80, how much do 9 kites cost? (a) ₹720 (b) ₹85 (c) ₹200 (d) ₹180
  23. 23.₹175 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹175 (b) ₹35 (c) ₹140 (d) ₹141
  24. 24.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 5 days (d) 14 days
  25. 25.If 3 notebooks cost ₹39, how much do 12 notebooks cost? (a) ₹169 (b) ₹48 (c) ₹156 (d) ₹468
  26. 26.If 3 pens cost ₹24, how much do 6 pens cost? (a) ₹48 (b) ₹144 (c) ₹27 (d) ₹56
  27. 27.₹658 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹235 (d) ₹423
  28. 28.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹116 (d) ₹58
  29. 29.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹85 (b) ₹68 (c) ₹17 (d) ₹102
  30. 30.If 5 pens cost ₹80, how much do 9 pens cost? (a) ₹160 (b) ₹720 (c) ₹144 (d) ₹84
  31. 31.If 7 pens cost ₹77, how much do 12 pens cost? (a) ₹143 (b) ₹924 (c) ₹132 (d) ₹82
  32. 32.If 2 notebooks cost ₹50, how much do 4 notebooks cost? (a) ₹125 (b) ₹52 (c) ₹200 (d) ₹100
  33. 33.₹235 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹47 (b) ₹189 (c) ₹235 (d) ₹188
  34. 34.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 4 days (d) 3 days
  35. 35.₹341 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹31 (b) ₹310 (c) ₹279 (d) ₹62
  36. 36.If 9 notebooks cost ₹81, how much do 10 notebooks cost? (a) ₹82 (b) ₹99 (c) ₹90 (d) ₹810
  37. 37.If 8 kites cost ₹144, how much do 11 kites cost? (a) ₹216 (b) ₹1584 (c) ₹147 (d) ₹198
  38. 38.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 45 days (d) 5 days
  39. 39.If 9 kites cost ₹45, how much do 6 kites cost? (a) ₹35 (b) ₹30 (c) ₹42 (d) ₹270
  40. 40.If 5 kites cost ₹75, how much do 8 kites cost? (a) ₹120 (b) ₹78 (c) ₹135 (d) ₹600

Answer key

  1. ₹333
  2. ₹50
  3. ₹126
  4. 36 days
  5. ₹33
  6. 20 days
  7. ₹8
  8. ₹140
  9. ₹42
  10. ₹119
  11. ₹114
  12. 7 days
  13. ₹80
  14. 24 days
  15. ₹42
  16. ₹176
  17. ₹245
  18. ₹24
  19. 16 days
  20. 2 days
  21. ₹174
  22. ₹180
  23. ₹140
  24. 14 days
  25. ₹156
  26. ₹48
  27. ₹423
  28. ₹87
  29. ₹85
  30. ₹144
  31. ₹132
  32. ₹100
  33. ₹188
  34. 3 days
  35. ₹279
  36. ₹90
  37. ₹198
  38. 45 days
  39. ₹30
  40. ₹120

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