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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 104 · 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.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹56 (b) ₹40 (c) ₹8 (d) ₹48
  2. 2.₹55 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹45 (d) ₹55
  3. 3.If 5 kites cost ₹50, how much do 2 kites cost? (a) ₹30 (b) ₹20 (c) ₹100 (d) ₹47
  4. 4.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 6 days (d) 8 days
  5. 5.If 3 kites cost ₹15, how much do 12 kites cost? (a) ₹60 (b) ₹65 (c) ₹24 (d) ₹180
  6. 6.If 7 pens cost ₹140, how much do 5 pens cost? (a) ₹120 (b) ₹700 (c) ₹100 (d) ₹138
  7. 7.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 28 days (d) 7 days
  8. 8.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹96 (b) ₹108 (c) ₹120 (d) ₹24
  9. 9.If 9 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹40 (b) ₹25 (c) ₹180 (d) ₹20
  10. 10.If 3 pens cost ₹54, how much do 6 pens cost? (a) ₹324 (b) ₹57 (c) ₹126 (d) ₹108
  11. 11.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹104 (c) ₹13 (d) ₹65
  12. 12.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹9 (b) ₹36 (c) ₹72 (d) ₹63
  13. 13.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹105 (d) ₹35
  14. 14.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 3 days (d) 9 days
  15. 15.If 6 mangoes cost ₹48, how much do 3 mangoes cost? (a) ₹144 (b) ₹32 (c) ₹45 (d) ₹24
  16. 16.If 3 mangoes cost ₹21, how much do 6 mangoes cost? (a) ₹49 (b) ₹24 (c) ₹42 (d) ₹126
  17. 17.₹168 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹105 (b) ₹63 (c) ₹84 (d) ₹21
  18. 18.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹10 (b) ₹90 (c) ₹55 (d) ₹20
  19. 19.If 3 notebooks cost ₹21, how much do 7 notebooks cost? (a) ₹147 (b) ₹49 (c) ₹25 (d) ₹56
  20. 20.₹350 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹175 (b) ₹50 (c) ₹300 (d) ₹350
  21. 21.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 13 days (d) 22 days
  22. 22.If 2 mangoes cost ₹18, how much do 10 mangoes cost? (a) ₹99 (b) ₹90 (c) ₹180 (d) ₹26
  23. 23.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹84 (b) ₹14 (c) ₹98 (d) ₹70
  24. 24.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹24 (c) ₹18 (d) ₹12
  25. 25.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹45 (d) ₹27
  26. 26.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 36 days (d) 5 days
  27. 27.If 5 notebooks cost ₹20, how much do 7 notebooks cost? (a) ₹140 (b) ₹22 (c) ₹32 (d) ₹28
  28. 28.If 7 kites cost ₹28, how much do 2 kites cost? (a) ₹23 (b) ₹12 (c) ₹8 (d) ₹56
  29. 29.If 2 pens cost ₹34, how much do 5 pens cost? (a) ₹85 (b) ₹102 (c) ₹170 (d) ₹37
  30. 30.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 9 days (d) 10 days
  31. 31.If 9 notebooks cost ₹180, how much do 10 notebooks cost? (a) ₹220 (b) ₹200 (c) ₹1800 (d) ₹181
  32. 32.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 7 days (d) 10 days
  33. 33.If 4 kites cost ₹96, how much do 2 kites cost? (a) ₹72 (b) ₹94 (c) ₹48 (d) ₹192
  34. 34.If 7 notebooks cost ₹49, how much do 8 notebooks cost? (a) ₹63 (b) ₹392 (c) ₹56 (d) ₹50
  35. 35.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 9 days (d) 11 days
  36. 36.If 5 mangoes cost ₹70, how much do 10 mangoes cost? (a) ₹154 (b) ₹700 (c) ₹75 (d) ₹140
  37. 37.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 8 days (d) 10 days
  38. 38.If 2 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹31 (b) ₹140 (c) ₹70 (d) ₹84
  39. 39.If 2 mangoes cost ₹50, how much do 8 mangoes cost? (a) ₹225 (b) ₹200 (c) ₹56 (d) ₹400
  40. 40.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹112 (b) ₹28 (c) ₹84 (d) ₹98

Answer key

  1. ₹56
  2. ₹44
  3. ₹20
  4. 8 days
  5. ₹60
  6. ₹100
  7. 7 days
  8. ₹120
  9. ₹20
  10. ₹108
  11. ₹104
  12. ₹63
  13. ₹140
  14. 3 days
  15. ₹24
  16. ₹42
  17. ₹105
  18. ₹90
  19. ₹49
  20. ₹300
  21. 21 days
  22. ₹90
  23. ₹98
  24. ₹24
  25. ₹36
  26. 35 days
  27. ₹28
  28. ₹8
  29. ₹85
  30. 9 days
  31. ₹200
  32. 10 days
  33. ₹48
  34. ₹56
  35. 16 days
  36. ₹140
  37. 10 days
  38. ₹70
  39. ₹200
  40. ₹112

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