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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 211 · 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 4 mangoes cost ₹20, how much do 11 mangoes cost? (a) ₹27 (b) ₹60 (c) ₹220 (d) ₹55
  2. 2.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 7 days (c) 17 days (d) 33 days
  3. 3.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 11 days (d) 16 days
  4. 4.If 7 pens cost ₹175, how much do 6 pens cost? (a) ₹175 (b) ₹1050 (c) ₹174 (d) ₹150
  5. 5.If 5 kites cost ₹95, how much do 4 kites cost? (a) ₹94 (b) ₹380 (c) ₹95 (d) ₹76
  6. 6.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
  7. 7.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 4 days (d) 15 days
  8. 8.If 9 pens cost ₹180, how much do 10 pens cost? (a) ₹220 (b) ₹200 (c) ₹181 (d) ₹1800
  9. 9.If 6 mangoes cost ₹42, how much do 3 mangoes cost? (a) ₹21 (b) ₹39 (c) ₹28 (d) ₹126
  10. 10.If 6 kites cost ₹120, how much do 7 kites cost? (a) ₹160 (b) ₹121 (c) ₹840 (d) ₹140
  11. 11.If 2 kites cost ₹16, how much do 4 kites cost? (a) ₹18 (b) ₹40 (c) ₹32 (d) ₹64
  12. 12.If 3 notebooks cost ₹33, how much do 12 notebooks cost? (a) ₹396 (b) ₹132 (c) ₹143 (d) ₹42
  13. 13.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹24 (d) ₹72
  14. 14.If 3 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹96 (b) ₹25 (c) ₹32 (d) ₹40
  15. 15.If 4 notebooks cost ₹32, how much do 10 notebooks cost? (a) ₹38 (b) ₹80 (c) ₹320 (d) ₹88
  16. 16.If 4 pens cost ₹28, how much do 7 pens cost? (a) ₹196 (b) ₹56 (c) ₹31 (d) ₹49
  17. 17.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹351 (b) ₹195 (c) ₹39 (d) ₹273
  18. 18.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 9 days (d) 10 days
  19. 19.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 7 days (d) 6 days
  20. 20.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 17 days (d) 22 days
  21. 21.If 6 kites cost ₹144, how much do 7 kites cost? (a) ₹1008 (b) ₹145 (c) ₹168 (d) ₹192
  22. 22.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
  23. 23.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 10 days (d) 6 days
  24. 24.If 3 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹33 (b) ₹96 (c) ₹104 (d) ₹288
  25. 25.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹114 (d) ₹133
  26. 26.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 7 days (d) 28 days
  27. 27.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 7 days (d) 6 days
  28. 28.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 23 days (c) 5 days (d) 7 days
  29. 29.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 18 days (d) 10 days
  30. 30.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹77 (b) ₹99 (c) ₹11 (d) ₹55
  31. 31.If 4 pens cost ₹24, how much do 11 pens cost? (a) ₹72 (b) ₹31 (c) ₹264 (d) ₹66
  32. 32.If 6 kites cost ₹48, how much do 7 kites cost? (a) ₹336 (b) ₹56 (c) ₹49 (d) ₹64
  33. 33.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 20 days (c) 42 days (d) 8 days
  34. 34.If 7 kites cost ₹168, how much do 6 kites cost? (a) ₹144 (b) ₹168 (c) ₹167 (d) ₹1008
  35. 35.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 20 days (c) 12 days (d) 5 days
  36. 36.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹144 (b) ₹288 (c) ₹252 (d) ₹36
  37. 37.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹172 (d) ₹129
  38. 38.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹75 (c) ₹15 (d) ₹90
  39. 39.If 3 notebooks cost ₹18, how much do 2 notebooks cost? (a) ₹36 (b) ₹17 (c) ₹18 (d) ₹12
  40. 40.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹120 (b) ₹165 (c) ₹30 (d) ₹210

Answer key

  1. ₹55
  2. 32 days
  3. 15 days
  4. ₹150
  5. ₹76
  6. 39 days
  7. 14 days
  8. ₹200
  9. ₹21
  10. ₹140
  11. ₹32
  12. ₹132
  13. ₹72
  14. ₹32
  15. ₹80
  16. ₹49
  17. ₹351
  18. 10 days
  19. 6 days
  20. 21 days
  21. ₹168
  22. 3 days
  23. 6 days
  24. ₹96
  25. ₹133
  26. 28 days
  27. 6 days
  28. 5 days
  29. 8 days
  30. ₹99
  31. ₹66
  32. ₹56
  33. 42 days
  34. ₹144
  35. 20 days
  36. ₹252
  37. ₹215
  38. ₹90
  39. ₹12
  40. ₹210

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