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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 93 · 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 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 17 days
  2. 2.₹187 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹68 (b) ₹136 (c) ₹17 (d) ₹119
  3. 3.If 2 pens cost ₹46, how much do 11 pens cost? (a) ₹276 (b) ₹253 (c) ₹55 (d) ₹506
  4. 4.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 18 days
  5. 5.₹138 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹69 (d) ₹92
  6. 6.₹160 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹160 (d) ₹140
  7. 7.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
  8. 8.7 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
  9. 9.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 11 days
  10. 10.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹196 (d) ₹126
  11. 11.₹196 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹126 (d) ₹98
  12. 12.If 2 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹108 (b) ₹54 (c) ₹60 (d) ₹19
  13. 13.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 4 days (d) 27 days
  14. 14.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹60 (b) ₹270 (c) ₹30 (d) ₹165
  15. 15.If 3 mangoes cost ₹9, how much do 5 mangoes cost? (a) ₹45 (b) ₹11 (c) ₹15 (d) ₹18
  16. 16.If 5 pens cost ₹100, how much do 10 pens cost? (a) ₹105 (b) ₹1000 (c) ₹200 (d) ₹220
  17. 17.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹55 (d) ₹33
  18. 18.₹204 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹102 (b) ₹204 (c) ₹170 (d) ₹34
  19. 19.If 6 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹36 (b) ₹52 (c) ₹45 (d) ₹216
  20. 20.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 33 days (c) 2 days (d) 32 days
  21. 21.₹240 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹120 (d) ₹240
  22. 22.If 7 mangoes cost ₹56, how much do 2 mangoes cost? (a) ₹112 (b) ₹24 (c) ₹51 (d) ₹16
  23. 23.₹90 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹75 (d) ₹45
  24. 24.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 11 days (c) 4 days (d) 5 days
  25. 25.If 5 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹118 (b) ₹360 (c) ₹72 (d) ₹96
  26. 26.If 6 kites cost ₹108, how much do 7 kites cost? (a) ₹109 (b) ₹756 (c) ₹126 (d) ₹144
  27. 27.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹20 (c) ₹100 (d) ₹140
  28. 28.If 2 mangoes cost ₹10, how much do 9 mangoes cost? (a) ₹50 (b) ₹90 (c) ₹17 (d) ₹45
  29. 29.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
  30. 30.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹266 (b) ₹190 (c) ₹342 (d) ₹38
  31. 31.If 7 kites cost ₹126, how much do 6 kites cost? (a) ₹126 (b) ₹108 (c) ₹756 (d) ₹125
  32. 32.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 8 days (d) 12 days
  33. 33.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹25 (d) ₹20
  34. 34.6 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 25 days (c) 9 days (d) 19 days
  35. 35.If 5 mangoes cost ₹65, how much do 4 mangoes cost? (a) ₹65 (b) ₹260 (c) ₹52 (d) ₹64
  36. 36.If 5 pens cost ₹85, how much do 10 pens cost? (a) ₹850 (b) ₹187 (c) ₹170 (d) ₹90
  37. 37.If 2 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹51 (b) ₹75 (c) ₹100 (d) ₹150
  38. 38.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹99 (b) ₹88 (c) ₹33 (d) ₹11
  39. 39.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 12 days (d) 1 day
  40. 40.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹230 (b) ₹276 (c) ₹46 (d) ₹138

Answer key

  1. 5 days
  2. ₹119
  3. ₹253
  4. 6 days
  5. ₹92
  6. ₹140
  7. 5 days
  8. 49 days
  9. 3 days
  10. ₹196
  11. ₹126
  12. ₹54
  13. 3 days
  14. ₹270
  15. ₹15
  16. ₹200
  17. ₹55
  18. ₹170
  19. ₹36
  20. 32 days
  21. ₹200
  22. ₹16
  23. ₹75
  24. 5 days
  25. ₹72
  26. ₹126
  27. ₹140
  28. ₹45
  29. 3 days
  30. ₹342
  31. ₹108
  32. 20 days
  33. ₹25
  34. 9 days
  35. ₹52
  36. ₹170
  37. ₹75
  38. ₹88
  39. 3 days
  40. ₹230

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