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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 390 · 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.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹55 (d) ₹33
  2. 2.If 8 mangoes cost ₹160, how much do 6 mangoes cost? (a) ₹120 (b) ₹140 (c) ₹960 (d) ₹158
  3. 3.If 6 mangoes cost ₹72, how much do 8 mangoes cost? (a) ₹108 (b) ₹96 (c) ₹576 (d) ₹74
  4. 4.If 7 kites cost ₹105, how much do 4 kites cost? (a) ₹420 (b) ₹75 (c) ₹60 (d) ₹102
  5. 5.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹200 (c) ₹50 (d) ₹150
  6. 6.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹124 (d) ₹217
  7. 7.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 4 days (d) 10 days
  8. 8.If 6 pens cost ₹30, how much do 10 pens cost? (a) ₹50 (b) ₹55 (c) ₹34 (d) ₹300
  9. 9.If 4 kites cost ₹16, how much do 5 kites cost? (a) ₹20 (b) ₹17 (c) ₹80 (d) ₹24
  10. 10.If 7 mangoes cost ₹63, how much do 3 mangoes cost? (a) ₹189 (b) ₹36 (c) ₹27 (d) ₹59
  11. 11.If 2 mangoes cost ₹34, how much do 6 mangoes cost? (a) ₹38 (b) ₹204 (c) ₹119 (d) ₹102
  12. 12.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹176 (b) ₹132 (c) ₹44 (d) ₹154
  13. 13.If 6 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹432 (b) ₹72 (c) ₹51 (d) ₹80
  14. 14.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹32 (d) ₹72
  15. 15.If 7 notebooks cost ₹140, how much do 12 notebooks cost? (a) ₹145 (b) ₹1680 (c) ₹260 (d) ₹240
  16. 16.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹40 (c) ₹10 (d) ₹25
  17. 17.₹215 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹129 (d) ₹86
  18. 18.If 6 mangoes cost ₹108, how much do 12 mangoes cost? (a) ₹234 (b) ₹114 (c) ₹1296 (d) ₹216
  19. 19.If 3 kites cost ₹72, how much do 6 kites cost? (a) ₹75 (b) ₹144 (c) ₹432 (d) ₹168
  20. 20.If 9 notebooks cost ₹54, how much do 10 notebooks cost? (a) ₹60 (b) ₹55 (c) ₹540 (d) ₹66
  21. 21.If 4 kites cost ₹40, how much do 2 kites cost? (a) ₹30 (b) ₹80 (c) ₹20 (d) ₹38
  22. 22.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹12 (d) ₹24
  23. 23.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 10 days (d) 11 days
  24. 24.If 4 kites cost ₹76, how much do 6 kites cost? (a) ₹456 (b) ₹114 (c) ₹133 (d) ₹78
  25. 25.If 6 kites cost ₹54, how much do 11 kites cost? (a) ₹59 (b) ₹108 (c) ₹99 (d) ₹594
  26. 26.If 2 pens cost ₹34, how much do 12 pens cost? (a) ₹221 (b) ₹44 (c) ₹204 (d) ₹408
  27. 27.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 11 days (d) 13 days
  28. 28.If 4 mangoes cost ₹80, how much do 9 mangoes cost? (a) ₹200 (b) ₹720 (c) ₹85 (d) ₹180
  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 2 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹60 (b) ₹90 (c) ₹45 (d) ₹31
  31. 31.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 4 days (d) 5 days
  32. 32.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹105 (d) ₹75
  33. 33.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 11 days
  34. 34.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 10 days (d) 26 days
  35. 35.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹223 (b) ₹222 (c) ₹37 (d) ₹259
  36. 36.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 9 days (d) 15 days
  37. 37.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 4 days (d) 11 days
  38. 38.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 6 days (d) 8 days
  39. 39.If 4 mangoes cost ₹40, how much do 10 mangoes cost? (a) ₹400 (b) ₹110 (c) ₹100 (d) ₹46
  40. 40.₹288 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹144 (b) ₹64 (c) ₹224 (d) ₹32

Answer key

  1. ₹55
  2. ₹120
  3. ₹96
  4. ₹60
  5. ₹200
  6. ₹217
  7. 9 days
  8. ₹50
  9. ₹20
  10. ₹27
  11. ₹102
  12. ₹176
  13. ₹72
  14. ₹112
  15. ₹240
  16. ₹40
  17. ₹129
  18. ₹216
  19. ₹144
  20. ₹60
  21. ₹20
  22. ₹16
  23. 10 days
  24. ₹114
  25. ₹99
  26. ₹204
  27. 12 days
  28. ₹180
  29. 14 days
  30. ₹45
  31. 5 days
  32. ₹105
  33. 5 days
  34. 26 days
  35. ₹222
  36. 14 days
  37. 10 days
  38. 8 days
  39. ₹100
  40. ₹224

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