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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 582 · 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. 1.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 15 days (d) 11 days
  2. 2.If 4 mangoes cost ₹32, how much do 6 mangoes cost? (a) ₹34 (b) ₹192 (c) ₹56 (d) ₹48
  3. 3.8 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) 20 days (d) 56 days
  4. 4.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 6 days (d) 7 days
  5. 5.If 6 mangoes cost ₹30, how much do 11 mangoes cost? (a) ₹35 (b) ₹55 (c) ₹60 (d) ₹330
  6. 6.If 8 pens cost ₹32, how much do 7 pens cost? (a) ₹31 (b) ₹28 (c) ₹224 (d) ₹32
  7. 7.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹300 (b) ₹250 (c) ₹275 (d) ₹50
  8. 8.₹450 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹100 (b) ₹350 (c) ₹50 (d) ₹225
  9. 9.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 20 days (d) 6 days
  10. 10.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹39 (d) ₹104
  11. 11.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 13 days (d) 12 days
  12. 12.₹385 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹175 (d) ₹245
  13. 13.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹40 (d) ₹240
  14. 14.₹126 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹18 (c) ₹108 (d) ₹63
  15. 15.If 6 notebooks cost ₹42, how much do 4 notebooks cost? (a) ₹28 (b) ₹35 (c) ₹40 (d) ₹168
  16. 16.If 5 pens cost ₹25, how much do 2 pens cost? (a) ₹50 (b) ₹10 (c) ₹22 (d) ₹15
  17. 17.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹41 (b) ₹164 (c) ₹123 (d) ₹82
  18. 18.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 20 days (c) 5 days (d) 8 days
  19. 19.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹72 (b) ₹55 (c) ₹216 (d) ₹90
  20. 20.If 4 pens cost ₹60, how much do 5 pens cost? (a) ₹300 (b) ₹90 (c) ₹61 (d) ₹75
  21. 21.If 5 pens cost ₹45, how much do 8 pens cost? (a) ₹81 (b) ₹72 (c) ₹48 (d) ₹360
  22. 22.If 3 mangoes cost ₹21, how much do 9 mangoes cost? (a) ₹27 (b) ₹70 (c) ₹63 (d) ₹189
  23. 23.If 5 pens cost ₹75, how much do 7 pens cost? (a) ₹77 (b) ₹120 (c) ₹105 (d) ₹525
  24. 24.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹80 (d) ₹16
  25. 25.If 6 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹63 (b) ₹252 (c) ₹42 (d) ₹122
  26. 26.If 7 pens cost ₹140, how much do 10 pens cost? (a) ₹200 (b) ₹220 (c) ₹1400 (d) ₹143
  27. 27.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 39 days (d) 7 days
  28. 28.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 11 days
  29. 29.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 14 days (d) 15 days
  30. 30.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 5 days (d) 8 days
  31. 31.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹161 (d) ₹184
  32. 32.₹30 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹6 (b) ₹15 (c) ₹24 (d) ₹30
  33. 33.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹10 (b) ₹12 (c) ₹15 (d) ₹36
  34. 34.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹65 (b) ₹52 (c) ₹78 (d) ₹26
  35. 35.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
  36. 36.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹60 (c) ₹20 (d) ₹80
  37. 37.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 3 days (d) 48 days
  38. 38.If 4 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹220 (b) ₹55 (c) ₹66 (d) ₹45
  39. 39.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹80 (b) ₹20 (c) ₹24 (d) ₹17
  40. 40.If 6 notebooks cost ₹66, how much do 4 notebooks cost? (a) ₹44 (b) ₹64 (c) ₹55 (d) ₹264

Answer key

  1. 15 days
  2. ₹48
  3. 56 days
  4. 7 days
  5. ₹55
  6. ₹28
  7. ₹300
  8. ₹350
  9. 5 days
  10. ₹104
  11. 12 days
  12. ₹210
  13. ₹240
  14. ₹108
  15. ₹28
  16. ₹10
  17. ₹123
  18. 20 days
  19. ₹72
  20. ₹75
  21. ₹72
  22. ₹63
  23. ₹105
  24. ₹80
  25. ₹42
  26. ₹200
  27. 39 days
  28. 14 days
  29. 14 days
  30. 8 days
  31. ₹161
  32. ₹24
  33. ₹12
  34. ₹78
  35. 6 days
  36. ₹60
  37. 48 days
  38. ₹55
  39. ₹20
  40. ₹44

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