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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 618 · 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.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹144 (c) ₹36 (d) ₹180
  2. 2.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹80 (b) ₹160 (c) ₹40 (d) ₹120
  3. 3.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹81 (b) ₹90 (c) ₹9 (d) ₹18
  4. 4.₹588 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹294 (b) ₹210 (c) ₹378 (d) ₹42
  5. 5.If 9 kites cost ₹90, how much do 10 kites cost? (a) ₹110 (b) ₹100 (c) ₹91 (d) ₹900
  6. 6.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 8 days (d) 2 days
  7. 7.If 2 pens cost ₹10, how much do 4 pens cost? (a) ₹12 (b) ₹40 (c) ₹25 (d) ₹20
  8. 8.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹15 (d) ₹14
  9. 9.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 9 days (d) 5 days
  10. 10.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 8 days (d) 6 days
  11. 11.If 4 notebooks cost ₹76, how much do 5 notebooks cost? (a) ₹95 (b) ₹77 (c) ₹114 (d) ₹380
  12. 12.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹16 (b) ₹25 (c) ₹60 (d) ₹20
  13. 13.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 20 days (d) 7 days
  14. 14.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
  15. 15.If 2 pens cost ₹30, how much do 6 pens cost? (a) ₹180 (b) ₹34 (c) ₹105 (d) ₹90
  16. 16.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹132 (b) ₹88 (c) ₹66 (d) ₹44
  17. 17.If 9 pens cost ₹45, how much do 8 pens cost? (a) ₹360 (b) ₹40 (c) ₹45 (d) ₹44
  18. 18.If 2 mangoes cost ₹6, how much do 9 mangoes cost? (a) ₹54 (b) ₹27 (c) ₹13 (d) ₹30
  19. 19.₹517 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹94 (b) ₹47 (c) ₹470 (d) ₹423
  20. 20.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹90 (b) ₹120 (c) ₹30 (d) ₹150
  21. 21.If 5 kites cost ₹85, how much do 6 kites cost? (a) ₹86 (b) ₹510 (c) ₹119 (d) ₹102
  22. 22.If 2 mangoes cost ₹38, how much do 3 mangoes cost? (a) ₹57 (b) ₹76 (c) ₹114 (d) ₹39
  23. 23.If 9 mangoes cost ₹216, how much do 4 mangoes cost? (a) ₹211 (b) ₹96 (c) ₹120 (d) ₹864
  24. 24.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 15 days (d) 27 days
  25. 25.If 6 kites cost ₹48, how much do 3 kites cost? (a) ₹45 (b) ₹144 (c) ₹32 (d) ₹24
  26. 26.If 7 mangoes cost ₹105, how much do 5 mangoes cost? (a) ₹525 (b) ₹90 (c) ₹75 (d) ₹103
  27. 27.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 6 days (d) 5 days
  28. 28.If 3 mangoes cost ₹39, how much do 4 mangoes cost? (a) ₹40 (b) ₹156 (c) ₹65 (d) ₹52
  29. 29.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹396 (c) ₹440 (d) ₹44
  30. 30.If 9 kites cost ₹117, how much do 4 kites cost? (a) ₹112 (b) ₹468 (c) ₹52 (d) ₹65
  31. 31.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
  32. 32.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 21 days (c) 22 days (d) 9 days
  33. 33.If 4 pens cost ₹44, how much do 9 pens cost? (a) ₹49 (b) ₹396 (c) ₹99 (d) ₹110
  34. 34.If 3 pens cost ₹18, how much do 8 pens cost? (a) ₹144 (b) ₹48 (c) ₹54 (d) ₹23
  35. 35.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 5 days (d) 4 days
  36. 36.If 3 mangoes cost ₹15, how much do 7 mangoes cost? (a) ₹35 (b) ₹40 (c) ₹19 (d) ₹105
  37. 37.If 2 mangoes cost ₹8, how much do 10 mangoes cost? (a) ₹44 (b) ₹40 (c) ₹80 (d) ₹16
  38. 38.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 6 days
  39. 39.If 5 mangoes cost ₹75, how much do 2 mangoes cost? (a) ₹45 (b) ₹150 (c) ₹30 (d) ₹72
  40. 40.If 3 pens cost ₹9, how much do 11 pens cost? (a) ₹36 (b) ₹99 (c) ₹17 (d) ₹33

Answer key

  1. ₹180
  2. ₹120
  3. ₹81
  4. ₹378
  5. ₹100
  6. 2 days
  7. ₹20
  8. ₹14
  9. 45 days
  10. 7 days
  11. ₹95
  12. ₹20
  13. 5 days
  14. 9 days
  15. ₹90
  16. ₹88
  17. ₹40
  18. ₹27
  19. ₹423
  20. ₹150
  21. ₹102
  22. ₹57
  23. ₹96
  24. 3 days
  25. ₹24
  26. ₹75
  27. 6 days
  28. ₹52
  29. ₹396
  30. ₹52
  31. 5 days
  32. 21 days
  33. ₹99
  34. ₹48
  35. 9 days
  36. ₹35
  37. ₹40
  38. 5 days
  39. ₹30
  40. ₹33

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