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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 6 · 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. 1.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 10 days (d) 11 days
  2. 2.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 11 days (d) 10 days
  3. 3.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹21 (c) ₹14 (d) ₹7
  4. 4.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹155 (c) ₹279 (d) ₹31
  5. 5.5 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
  6. 6.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹50 (c) ₹60 (d) ₹10
  7. 7.If 9 kites cost ₹135, how much do 3 kites cost? (a) ₹405 (b) ₹129 (c) ₹60 (d) ₹45
  8. 8.If 6 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹84 (b) ₹91 (c) ₹48 (d) ₹504
  9. 9.If 3 notebooks cost ₹57, how much do 2 notebooks cost? (a) ₹57 (b) ₹114 (c) ₹38 (d) ₹56
  10. 10.If 2 pens cost ₹18, how much do 3 pens cost? (a) ₹27 (b) ₹19 (c) ₹54 (d) ₹36
  11. 11.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 4 days
  12. 12.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹91 (b) ₹112 (c) ₹70 (d) ₹14
  13. 13.If 5 pens cost ₹95, how much do 6 pens cost? (a) ₹570 (b) ₹114 (c) ₹96 (d) ₹133
  14. 14.If 3 kites cost ₹9, how much do 7 kites cost? (a) ₹13 (b) ₹24 (c) ₹21 (d) ₹63
  15. 15.If 8 pens cost ₹88, how much do 12 pens cost? (a) ₹132 (b) ₹92 (c) ₹143 (d) ₹1056
  16. 16.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹105 (b) ₹140 (c) ₹70 (d) ₹35
  17. 17.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 12 days (d) 8 days
  18. 18.If 7 pens cost ₹63, how much do 10 pens cost? (a) ₹99 (b) ₹66 (c) ₹630 (d) ₹90
  19. 19.₹154 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹56 (c) ₹14 (d) ₹98
  20. 20.₹319 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹261 (b) ₹290 (c) ₹58 (d) ₹29
  21. 21.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 13 days (d) 7 days
  22. 22.If 2 mangoes cost ₹26, how much do 3 mangoes cost? (a) ₹52 (b) ₹78 (c) ₹27 (d) ₹39
  23. 23.If 6 notebooks cost ₹114, how much do 7 notebooks cost? (a) ₹115 (b) ₹798 (c) ₹133 (d) ₹152
  24. 24.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹126 (b) ₹42 (c) ₹231 (d) ₹336
  25. 25.If 7 kites cost ₹126, how much do 6 kites cost? (a) ₹125 (b) ₹756 (c) ₹126 (d) ₹108
  26. 26.If 6 kites cost ₹144, how much do 5 kites cost? (a) ₹720 (b) ₹144 (c) ₹120 (d) ₹143
  27. 27.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 11 days (d) 17 days
  28. 28.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 4 days (d) 3 days
  29. 29.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹210 (d) ₹140
  30. 30.If 8 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹360 (b) ₹60 (c) ₹115 (d) ₹45
  31. 31.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 39 days (c) 40 days (d) 19 days
  32. 32.If 5 pens cost ₹100, how much do 11 pens cost? (a) ₹106 (b) ₹240 (c) ₹220 (d) ₹1100
  33. 33.If 6 kites cost ₹108, how much do 8 kites cost? (a) ₹864 (b) ₹144 (c) ₹162 (d) ₹110
  34. 34.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹192 (d) ₹144
  35. 35.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹205 (b) ₹246 (c) ₹287 (d) ₹41
  36. 36.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 10 days (d) 4 days
  37. 37.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹111 (b) ₹660 (c) ₹154 (d) ₹132
  38. 38.If 4 kites cost ₹32, how much do 2 kites cost? (a) ₹30 (b) ₹64 (c) ₹16 (d) ₹24
  39. 39.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 21 days (c) 4 days (d) 48 days
  40. 40.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹16 (b) ₹56 (c) ₹64 (d) ₹48

Answer key

  1. 10 days
  2. 10 days
  3. ₹21
  4. ₹279
  5. 5 days
  6. ₹60
  7. ₹45
  8. ₹84
  9. ₹38
  10. ₹27
  11. 8 days
  12. ₹112
  13. ₹114
  14. ₹21
  15. ₹132
  16. ₹105
  17. 12 days
  18. ₹90
  19. ₹98
  20. ₹261
  21. 6 days
  22. ₹39
  23. ₹133
  24. ₹336
  25. ₹108
  26. ₹120
  27. 12 days
  28. 3 days
  29. ₹175
  30. ₹45
  31. 39 days
  32. ₹220
  33. ₹144
  34. ₹144
  35. ₹287
  36. 4 days
  37. ₹132
  38. ₹16
  39. 3 days
  40. ₹64

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