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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 922 · 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.₹264 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹24 (b) ₹132 (c) ₹192 (d) ₹72
  2. 2.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 12 days (d) 13 days
  3. 3.If 8 mangoes cost ₹40, how much do 5 mangoes cost? (a) ₹30 (b) ₹37 (c) ₹200 (d) ₹25
  4. 4.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹48 (b) ₹288 (c) ₹36 (d) ₹91
  5. 5.If 3 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹56 (b) ₹43 (c) ₹168 (d) ₹70
  6. 6.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹11 (c) ₹10 (d) ₹5
  7. 7.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
  8. 8.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 16 days (d) 9 days
  9. 9.If 5 mangoes cost ₹20, how much do 8 mangoes cost? (a) ₹32 (b) ₹160 (c) ₹36 (d) ₹23
  10. 10.₹42 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹35 (b) ₹21 (c) ₹42 (d) ₹7
  11. 11.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 9 days (c) 19 days (d) 4 days
  12. 12.If 8 kites cost ₹152, how much do 5 kites cost? (a) ₹95 (b) ₹114 (c) ₹760 (d) ₹149
  13. 13.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹84 (b) ₹120 (c) ₹24 (d) ₹48
  14. 14.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹125 (b) ₹175 (c) ₹25 (d) ₹150
  15. 15.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 13 days (d) 14 days
  16. 16.If 2 kites cost ₹26, how much do 9 kites cost? (a) ₹33 (b) ₹234 (c) ₹117 (d) ₹130
  17. 17.₹308 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹154 (d) ₹132
  18. 18.If 3 pens cost ₹60, how much do 10 pens cost? (a) ₹67 (b) ₹200 (c) ₹600 (d) ₹220
  19. 19.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹328 (d) ₹205
  20. 20.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 11 days (d) 10 days
  21. 21.If 7 mangoes cost ₹112, how much do 4 mangoes cost? (a) ₹80 (b) ₹448 (c) ₹109 (d) ₹64
  22. 22.If 5 mangoes cost ₹105, how much do 7 mangoes cost? (a) ₹168 (b) ₹735 (c) ₹147 (d) ₹107
  23. 23.If 9 notebooks cost ₹81, how much do 3 notebooks cost? (a) ₹36 (b) ₹243 (c) ₹75 (d) ₹27
  24. 24.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 63 days (c) 21 days (d) 7 days
  25. 25.₹209 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹133 (d) ₹95
  26. 26.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 21 days (d) 45 days
  27. 27.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 6 days
  28. 28.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 10 days (d) 4 days
  29. 29.₹105 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹75 (b) ₹90 (c) ₹15 (d) ₹30
  30. 30.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹18 (b) ₹9 (c) ₹7 (d) ₹12
  31. 31.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 3 days (d) 9 days
  32. 32.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 45 days (d) 21 days
  33. 33.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 7 days (c) 39 days (d) 19 days
  34. 34.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹6 (b) ₹54 (c) ₹42 (d) ₹30
  35. 35.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 10 days (d) 12 days
  36. 36.If 4 notebooks cost ₹92, how much do 6 notebooks cost? (a) ₹552 (b) ₹94 (c) ₹161 (d) ₹138
  37. 37.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 8 days (d) 24 days
  38. 38.If 5 pens cost ₹100, how much do 2 pens cost? (a) ₹60 (b) ₹97 (c) ₹40 (d) ₹200
  39. 39.If 8 pens cost ₹120, how much do 7 pens cost? (a) ₹119 (b) ₹840 (c) ₹105 (d) ₹120
  40. 40.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 12 days (d) 18 days

Answer key

  1. ₹192
  2. 12 days
  3. ₹25
  4. ₹36
  5. ₹56
  6. ₹10
  7. 5 days
  8. 15 days
  9. ₹32
  10. ₹35
  11. 49 days
  12. ₹95
  13. ₹120
  14. ₹150
  15. 14 days
  16. ₹117
  17. ₹176
  18. ₹200
  19. ₹328
  20. 10 days
  21. ₹64
  22. ₹147
  23. ₹27
  24. 63 days
  25. ₹114
  26. 5 days
  27. 8 days
  28. 14 days
  29. ₹75
  30. ₹9
  31. 3 days
  32. 45 days
  33. 39 days
  34. ₹54
  35. 12 days
  36. ₹138
  37. 6 days
  38. ₹40
  39. ₹105
  40. 24 days

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