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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 450 · 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.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹14 (b) ₹63 (c) ₹70 (d) ₹56
  2. 2.If 6 mangoes cost ₹66, how much do 2 mangoes cost? (a) ₹22 (b) ₹62 (c) ₹132 (d) ₹33
  3. 3.If 5 mangoes cost ₹125, how much do 9 mangoes cost? (a) ₹1125 (b) ₹225 (c) ₹129 (d) ₹250
  4. 4.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 1 day (d) 8 days
  5. 5.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 15 days (d) 12 days
  6. 6.If 3 kites cost ₹27, how much do 5 kites cost? (a) ₹45 (b) ₹54 (c) ₹29 (d) ₹135
  7. 7.If 8 pens cost ₹24, how much do 10 pens cost? (a) ₹30 (b) ₹240 (c) ₹26 (d) ₹33
  8. 8.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 28 days (d) 26 days
  9. 9.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 17 days
  10. 10.If 8 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹96 (b) ₹12 (c) ₹15 (d) ₹20
  11. 11.If 8 pens cost ₹56, how much do 9 pens cost? (a) ₹504 (b) ₹70 (c) ₹57 (d) ₹63
  12. 12.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 9 days
  13. 13.If 9 pens cost ₹108, how much do 6 pens cost? (a) ₹72 (b) ₹648 (c) ₹105 (d) ₹84
  14. 14.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 5 days (d) 8 days
  15. 15.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹400 (d) ₹360
  16. 16.If 5 kites cost ₹100, how much do 7 kites cost? (a) ₹102 (b) ₹700 (c) ₹140 (d) ₹160
  17. 17.If 8 notebooks cost ₹136, how much do 10 notebooks cost? (a) ₹187 (b) ₹138 (c) ₹170 (d) ₹1360
  18. 18.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹5 (c) ₹25 (d) ₹45
  19. 19.If 8 mangoes cost ₹64, how much do 4 mangoes cost? (a) ₹32 (b) ₹256 (c) ₹40 (d) ₹60
  20. 20.If 9 notebooks cost ₹180, how much do 7 notebooks cost? (a) ₹1260 (b) ₹160 (c) ₹178 (d) ₹140
  21. 21.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 12 days (d) 18 days
  22. 22.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹43 (b) ₹344 (c) ₹172 (d) ₹301
  23. 23.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 4 days (d) 5 days
  24. 24.If 3 pens cost ₹45, how much do 5 pens cost? (a) ₹47 (b) ₹225 (c) ₹75 (d) ₹90
  25. 25.If 2 kites cost ₹26, how much do 10 kites cost? (a) ₹143 (b) ₹260 (c) ₹34 (d) ₹130
  26. 26.If 2 pens cost ₹50, how much do 9 pens cost? (a) ₹450 (b) ₹57 (c) ₹225 (d) ₹250
  27. 27.If 3 mangoes cost ₹54, how much do 12 mangoes cost? (a) ₹216 (b) ₹63 (c) ₹234 (d) ₹648
  28. 28.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 7 days (d) 9 days
  29. 29.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹310 (d) ₹279
  30. 30.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹10 (b) ₹80 (c) ₹65 (d) ₹50
  31. 31.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 8 days (d) 12 days
  32. 32.If 2 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹37 (b) ₹54 (c) ₹72 (d) ₹108
  33. 33.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹160 (d) ₹130
  34. 34.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 17 days (d) 2 days
  35. 35.If 9 pens cost ₹27, how much do 6 pens cost? (a) ₹162 (b) ₹21 (c) ₹18 (d) ₹24
  36. 36.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 12 days (c) 18 days (d) 30 days
  37. 37.₹176 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹110 (b) ₹88 (c) ₹66 (d) ₹22
  38. 38.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹44 (b) ₹32 (c) ₹8 (d) ₹56
  39. 39.If 8 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹21 (b) ₹120 (c) ₹18 (d) ₹15
  40. 40.If 4 notebooks cost ₹80, how much do 9 notebooks cost? (a) ₹180 (b) ₹200 (c) ₹85 (d) ₹720

Answer key

  1. ₹70
  2. ₹22
  3. ₹225
  4. 2 days
  5. 15 days
  6. ₹45
  7. ₹30
  8. 27 days
  9. 21 days
  10. ₹12
  11. ₹63
  12. 8 days
  13. ₹72
  14. 9 days
  15. ₹360
  16. ₹140
  17. ₹170
  18. ₹45
  19. ₹32
  20. ₹140
  21. 10 days
  22. ₹301
  23. 5 days
  24. ₹75
  25. ₹130
  26. ₹225
  27. ₹216
  28. 8 days
  29. ₹279
  30. ₹80
  31. 12 days
  32. ₹54
  33. ₹160
  34. 3 days
  35. ₹18
  36. 30 days
  37. ₹110
  38. ₹56
  39. ₹15
  40. ₹180

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