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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 195 · 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.If 5 pens cost ₹20, how much do 6 pens cost? (a) ₹28 (b) ₹120 (c) ₹24 (d) ₹21
  2. 2.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 3 days (d) 2 days
  3. 3.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 53 days (c) 19 days (d) 52 days
  4. 4.If 8 pens cost ₹96, how much do 5 pens cost? (a) ₹72 (b) ₹480 (c) ₹60 (d) ₹93
  5. 5.If 3 mangoes cost ₹51, how much do 2 mangoes cost? (a) ₹51 (b) ₹102 (c) ₹50 (d) ₹34
  6. 6.If 8 mangoes cost ₹40, how much do 12 mangoes cost? (a) ₹65 (b) ₹44 (c) ₹60 (d) ₹480
  7. 7.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹164 (b) ₹123 (c) ₹41 (d) ₹82
  8. 8.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹68 (b) ₹51 (c) ₹34 (d) ₹17
  9. 9.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 49 days (d) 19 days
  10. 10.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 18 days (d) 5 days
  11. 11.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹125 (c) ₹175 (d) ₹25
  12. 12.If 6 kites cost ₹48, how much do 10 kites cost? (a) ₹52 (b) ₹480 (c) ₹80 (d) ₹88
  13. 13.₹418 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹38 (b) ₹342 (c) ₹209 (d) ₹76
  14. 14.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 16 days (d) 11 days
  15. 15.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 3 days (d) 2 days
  16. 16.If 7 pens cost ₹161, how much do 3 pens cost? (a) ₹69 (b) ₹92 (c) ₹157 (d) ₹483
  17. 17.If 4 kites cost ₹32, how much do 5 kites cost? (a) ₹48 (b) ₹40 (c) ₹160 (d) ₹33
  18. 18.If 9 mangoes cost ₹171, how much do 2 mangoes cost? (a) ₹342 (b) ₹38 (c) ₹164 (d) ₹57
  19. 19.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 27 days (d) 26 days
  20. 20.₹420 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹210 (b) ₹150 (c) ₹30 (d) ₹270
  21. 21.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹18 (c) ₹162 (d) ₹72
  22. 22.If 7 notebooks cost ₹105, how much do 4 notebooks cost? (a) ₹75 (b) ₹60 (c) ₹420 (d) ₹102
  23. 23.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 6 days
  24. 24.If 3 notebooks cost ₹21, how much do 2 notebooks cost? (a) ₹20 (b) ₹21 (c) ₹14 (d) ₹42
  25. 25.If 5 pens cost ₹25, how much do 6 pens cost? (a) ₹35 (b) ₹150 (c) ₹30 (d) ₹26
  26. 26.If 5 kites cost ₹40, how much do 9 kites cost? (a) ₹72 (b) ₹44 (c) ₹80 (d) ₹360
  27. 27.If 5 kites cost ₹85, how much do 3 kites cost? (a) ₹68 (b) ₹255 (c) ₹51 (d) ₹83
  28. 28.If 8 pens cost ₹160, how much do 2 pens cost? (a) ₹320 (b) ₹154 (c) ₹60 (d) ₹40
  29. 29.₹518 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹259 (b) ₹185 (c) ₹37 (d) ₹333
  30. 30.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹72 (c) ₹36 (d) ₹108
  31. 31.If 3 kites cost ₹21, how much do 9 kites cost? (a) ₹27 (b) ₹63 (c) ₹189 (d) ₹70
  32. 32.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹75 (d) ₹60
  33. 33.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 3 days (c) 46 days (d) 17 days
  34. 34.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 22 days (d) 21 days
  35. 35.If 5 pens cost ₹15, how much do 8 pens cost? (a) ₹120 (b) ₹18 (c) ₹27 (d) ₹24
  36. 36.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 12 days (c) 5 days (d) 7 days
  37. 37.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 55 days (b) 19 days (c) 54 days (d) 5 days
  38. 38.If 7 pens cost ₹168, how much do 6 pens cost? (a) ₹168 (b) ₹144 (c) ₹1008 (d) ₹167
  39. 39.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹85 (d) ₹51
  40. 40.If 6 notebooks cost ₹144, how much do 4 notebooks cost? (a) ₹576 (b) ₹120 (c) ₹142 (d) ₹96

Answer key

  1. ₹24
  2. 3 days
  3. 52 days
  4. ₹60
  5. ₹34
  6. ₹60
  7. ₹123
  8. ₹51
  9. 49 days
  10. 4 days
  11. ₹150
  12. ₹80
  13. ₹342
  14. 16 days
  15. 3 days
  16. ₹69
  17. ₹40
  18. ₹38
  19. 26 days
  20. ₹270
  21. ₹162
  22. ₹60
  23. 7 days
  24. ₹14
  25. ₹30
  26. ₹72
  27. ₹51
  28. ₹40
  29. ₹333
  30. ₹108
  31. ₹63
  32. ₹60
  33. 45 days
  34. 21 days
  35. ₹24
  36. 6 days
  37. 54 days
  38. ₹144
  39. ₹85
  40. ₹96

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