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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 378 · 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.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹52 (d) ₹39
  2. 2.₹363 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹330 (b) ₹66 (c) ₹33 (d) ₹297
  3. 3.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹9 (b) ₹63 (c) ₹45 (d) ₹54
  4. 4.If 2 pens cost ₹30, how much do 7 pens cost? (a) ₹210 (b) ₹120 (c) ₹35 (d) ₹105
  5. 5.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹238 (b) ₹170 (c) ₹204 (d) ₹34
  6. 6.If 6 mangoes cost ₹54, how much do 9 mangoes cost? (a) ₹57 (b) ₹81 (c) ₹486 (d) ₹90
  7. 7.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 13 days (d) 7 days
  8. 8.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹32 (c) ₹40 (d) ₹8
  9. 9.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 8 days (d) 15 days
  10. 10.If 2 pens cost ₹28, how much do 11 pens cost? (a) ₹168 (b) ₹37 (c) ₹308 (d) ₹154
  11. 11.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹123 (b) ₹205 (c) ₹41 (d) ₹287
  12. 12.If 3 kites cost ₹39, how much do 10 kites cost? (a) ₹143 (b) ₹130 (c) ₹390 (d) ₹46
  13. 13.If 9 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹78 (b) ₹72 (c) ₹648 (d) ₹57
  14. 14.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 2 days
  15. 15.If 8 notebooks cost ₹80, how much do 10 notebooks cost? (a) ₹110 (b) ₹82 (c) ₹100 (d) ₹800
  16. 16.If 5 pens cost ₹15, how much do 3 pens cost? (a) ₹45 (b) ₹12 (c) ₹13 (d) ₹9
  17. 17.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 6 days (d) 18 days
  18. 18.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹110 (b) ₹99 (c) ₹44 (d) ₹11
  19. 19.If 3 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹168 (b) ₹28 (c) ₹56 (d) ₹64
  20. 20.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹40 (b) ₹15 (c) ₹45 (d) ₹5
  21. 21.If 4 pens cost ₹80, how much do 5 pens cost? (a) ₹120 (b) ₹100 (c) ₹81 (d) ₹400
  22. 22.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 7 days (d) 18 days
  23. 23.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹54 (b) ₹12 (c) ₹48 (d) ₹60
  24. 24.If 9 mangoes cost ₹81, how much do 10 mangoes cost? (a) ₹82 (b) ₹810 (c) ₹90 (d) ₹99
  25. 25.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 56 days (d) 20 days
  26. 26.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 14 days (d) 22 days
  27. 27.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 20 days (d) 21 days
  28. 28.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹36 (b) ₹90 (c) ₹18 (d) ₹63
  29. 29.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹155 (b) ₹31 (c) ₹124 (d) ₹93
  30. 30.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 6 days (d) 24 days
  31. 31.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 4 days (d) 12 days
  32. 32.If 5 notebooks cost ₹100, how much do 9 notebooks cost? (a) ₹200 (b) ₹900 (c) ₹180 (d) ₹104
  33. 33.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 10 days (d) 14 days
  34. 34.If 4 kites cost ₹24, how much do 7 kites cost? (a) ₹27 (b) ₹168 (c) ₹48 (d) ₹42
  35. 35.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
  36. 36.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹185 (b) ₹222 (c) ₹37 (d) ₹259
  37. 37.If 7 pens cost ₹175, how much do 3 pens cost? (a) ₹75 (b) ₹525 (c) ₹100 (d) ₹171
  38. 38.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹126 (d) ₹108
  39. 39.If 6 kites cost ₹138, how much do 10 kites cost? (a) ₹1380 (b) ₹230 (c) ₹253 (d) ₹142
  40. 40.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 17 days (d) 32 days

Answer key

  1. ₹52
  2. ₹297
  3. ₹63
  4. ₹105
  5. ₹238
  6. ₹81
  7. 5 days
  8. ₹40
  9. 15 days
  10. ₹154
  11. ₹287
  12. ₹130
  13. ₹72
  14. 8 days
  15. ₹100
  16. ₹9
  17. 18 days
  18. ₹99
  19. ₹56
  20. ₹40
  21. ₹100
  22. 6 days
  23. ₹60
  24. ₹90
  25. 56 days
  26. 22 days
  27. 20 days
  28. ₹90
  29. ₹124
  30. 6 days
  31. 16 days
  32. ₹180
  33. 9 days
  34. ₹42
  35. 9 days
  36. ₹222
  37. ₹75
  38. ₹144
  39. ₹230
  40. 32 days

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