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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 615 · 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.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹140 (c) ₹35 (d) ₹175
  2. 2.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 13 days (d) 25 days
  3. 3.If 4 notebooks cost ₹28, how much do 10 notebooks cost? (a) ₹70 (b) ₹280 (c) ₹34 (d) ₹77
  4. 4.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹76 (b) ₹19 (c) ₹95 (d) ₹114
  5. 5.If 7 mangoes cost ₹175, how much do 8 mangoes cost? (a) ₹176 (b) ₹200 (c) ₹1400 (d) ₹225
  6. 6.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 13 days (d) 8 days
  7. 7.If 8 kites cost ₹32, how much do 3 kites cost? (a) ₹12 (b) ₹16 (c) ₹27 (d) ₹96
  8. 8.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 15 days (d) 11 days
  9. 9.₹92 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹23 (b) ₹46 (c) ₹92 (d) ₹69
  10. 10.If 9 pens cost ₹135, how much do 5 pens cost? (a) ₹131 (b) ₹75 (c) ₹90 (d) ₹675
  11. 11.If 3 kites cost ₹72, how much do 4 kites cost? (a) ₹73 (b) ₹96 (c) ₹288 (d) ₹120
  12. 12.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 12 days (d) 16 days
  13. 13.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 15 days (c) 27 days (d) 3 days
  14. 14.If 2 pens cost ₹18, how much do 4 pens cost? (a) ₹20 (b) ₹36 (c) ₹45 (d) ₹72
  15. 15.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹44 (b) ₹33 (c) ₹11 (d) ₹55
  16. 16.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 3 days (d) 21 days
  17. 17.If 2 pens cost ₹8, how much do 10 pens cost? (a) ₹44 (b) ₹80 (c) ₹40 (d) ₹16
  18. 18.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 21 days (d) 11 days
  19. 19.If 6 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹1008 (b) ₹192 (c) ₹145 (d) ₹168
  20. 20.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 1 day (c) 17 days (d) 3 days
  21. 21.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 8 days (d) 10 days
  22. 22.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹45 (d) ₹5
  23. 23.If 3 mangoes cost ₹39, how much do 8 mangoes cost? (a) ₹117 (b) ₹44 (c) ₹312 (d) ₹104
  24. 24.If 5 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹132 (b) ₹120 (c) ₹600 (d) ₹65
  25. 25.₹430 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹430 (b) ₹215 (c) ₹43 (d) ₹387
  26. 26.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹80 (b) ₹32 (c) ₹56 (d) ₹16
  27. 27.If 9 mangoes cost ₹81, how much do 3 mangoes cost? (a) ₹36 (b) ₹243 (c) ₹27 (d) ₹75
  28. 28.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 7 days (d) 18 days
  29. 29.If 8 pens cost ₹144, how much do 9 pens cost? (a) ₹145 (b) ₹1296 (c) ₹162 (d) ₹180
  30. 30.8 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
  31. 31.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹60 (d) ₹70
  32. 32.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹72 (c) ₹16 (d) ₹80
  33. 33.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 27 days (d) 13 days
  34. 34.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 49 days (d) 9 days
  35. 35.If 2 kites cost ₹12, how much do 3 kites cost? (a) ₹13 (b) ₹36 (c) ₹24 (d) ₹18
  36. 36.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹138 (b) ₹184 (c) ₹46 (d) ₹161
  37. 37.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹56 (b) ₹112 (c) ₹16 (d) ₹96
  38. 38.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹98 (b) ₹70 (c) ₹126 (d) ₹14
  39. 39.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 27 days (d) 5 days
  40. 40.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 3 days

Answer key

  1. ₹175
  2. 9 days
  3. ₹70
  4. ₹95
  5. ₹200
  6. 12 days
  7. ₹12
  8. 15 days
  9. ₹69
  10. ₹75
  11. ₹96
  12. 10 days
  13. 27 days
  14. ₹36
  15. ₹55
  16. 21 days
  17. ₹40
  18. 21 days
  19. ₹168
  20. 3 days
  21. 9 days
  22. ₹45
  23. ₹104
  24. ₹120
  25. ₹387
  26. ₹80
  27. ₹27
  28. 6 days
  29. ₹162
  30. 52 days
  31. ₹80
  32. ₹80
  33. 27 days
  34. 49 days
  35. ₹18
  36. ₹184
  37. ₹96
  38. ₹126
  39. 27 days
  40. 15 days

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