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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 720 · 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.₹340 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹306 (b) ₹170 (c) ₹340 (d) ₹34
  2. 2.If 2 pens cost ₹22, how much do 12 pens cost? (a) ₹264 (b) ₹132 (c) ₹143 (d) ₹32
  3. 3.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
  4. 4.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 3 days (d) 9 days
  5. 5.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹60 (b) ₹16 (c) ₹25 (d) ₹20
  6. 6.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 25 days (d) 13 days
  7. 7.If 7 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹78 (b) ₹504 (c) ₹72 (d) ₹47
  8. 8.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹188 (b) ₹376 (c) ₹47 (d) ₹329
  9. 9.If 7 mangoes cost ₹147, how much do 2 mangoes cost? (a) ₹142 (b) ₹294 (c) ₹42 (d) ₹63
  10. 10.If 5 pens cost ₹75, how much do 3 pens cost? (a) ₹225 (b) ₹73 (c) ₹45 (d) ₹60
  11. 11.If 6 kites cost ₹78, how much do 9 kites cost? (a) ₹81 (b) ₹702 (c) ₹117 (d) ₹130
  12. 12.If 6 mangoes cost ₹108, how much do 3 mangoes cost? (a) ₹54 (b) ₹105 (c) ₹72 (d) ₹324
  13. 13.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹108 (b) ₹53 (c) ₹54 (d) ₹36
  14. 14.If 2 pens cost ₹16, how much do 9 pens cost? (a) ₹80 (b) ₹23 (c) ₹144 (d) ₹72
  15. 15.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹18 (c) ₹144 (d) ₹90
  16. 16.If 5 kites cost ₹25, how much do 6 kites cost? (a) ₹26 (b) ₹150 (c) ₹30 (d) ₹35
  17. 17.If 3 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹96 (b) ₹84 (c) ₹252 (d) ₹40
  18. 18.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 7 days (d) 4 days
  19. 19.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 17 days (d) 5 days
  20. 20.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 16 days (d) 12 days
  21. 21.₹48 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹42 (d) ₹6
  22. 22.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹273 (c) ₹234 (d) ₹39
  23. 23.If 8 mangoes cost ₹184, how much do 3 mangoes cost? (a) ₹552 (b) ₹92 (c) ₹69 (d) ₹179
  24. 24.3 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) 4 days (d) 5 days
  25. 25.₹296 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹111 (b) ₹148 (c) ₹37 (d) ₹185
  26. 26.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹245 (d) ₹147
  27. 27.If 8 mangoes cost ₹184, how much do 9 mangoes cost? (a) ₹230 (b) ₹1656 (c) ₹207 (d) ₹185
  28. 28.If 6 kites cost ₹24, how much do 2 kites cost? (a) ₹12 (b) ₹48 (c) ₹8 (d) ₹20
  29. 29.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
  30. 30.If 6 kites cost ₹54, how much do 3 kites cost? (a) ₹27 (b) ₹162 (c) ₹36 (d) ₹51
  31. 31.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days
  32. 32.If 5 pens cost ₹80, how much do 4 pens cost? (a) ₹64 (b) ₹320 (c) ₹80 (d) ₹79
  33. 33.If 7 kites cost ₹147, how much do 2 kites cost? (a) ₹142 (b) ₹63 (c) ₹42 (d) ₹294
  34. 34.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 6 days
  35. 35.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹175 (b) ₹210 (c) ₹35 (d) ₹140
  36. 36.₹248 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹124 (b) ₹248 (c) ₹217 (d) ₹31
  37. 37.If 3 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹22 (b) ₹126 (c) ₹48 (d) ₹42
  38. 38.If 5 mangoes cost ₹35, how much do 4 mangoes cost? (a) ₹34 (b) ₹28 (c) ₹140 (d) ₹35
  39. 39.If 8 pens cost ₹192, how much do 5 pens cost? (a) ₹189 (b) ₹960 (c) ₹120 (d) ₹144
  40. 40.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 20 days (d) 21 days

Answer key

  1. ₹306
  2. ₹132
  3. 3 days
  4. 15 days
  5. ₹20
  6. 9 days
  7. ₹72
  8. ₹329
  9. ₹42
  10. ₹45
  11. ₹117
  12. ₹54
  13. ₹36
  14. ₹72
  15. ₹144
  16. ₹30
  17. ₹84
  18. 25 days
  19. 5 days
  20. 16 days
  21. ₹42
  22. ₹234
  23. ₹69
  24. 9 days
  25. ₹185
  26. ₹245
  27. ₹207
  28. ₹8
  29. 3 days
  30. ₹27
  31. 45 days
  32. ₹64
  33. ₹42
  34. 4 days
  35. ₹175
  36. ₹217
  37. ₹42
  38. ₹28
  39. ₹120
  40. 20 days

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