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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 796 · 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. 1.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 9 days (d) 8 days
  2. 2.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 7 days (c) 13 days (d) 4 days
  3. 3.If 9 notebooks cost ₹153, how much do 5 notebooks cost? (a) ₹765 (b) ₹149 (c) ₹102 (d) ₹85
  4. 4.If 4 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹44 (b) ₹117 (c) ₹432 (d) ₹108
  5. 5.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 3 days (d) 11 days
  6. 6.If 7 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹36 (b) ₹80 (c) ₹252 (d) ₹48
  7. 7.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹32 (b) ₹96 (c) ₹192 (d) ₹160
  8. 8.If 9 kites cost ₹45, how much do 3 kites cost? (a) ₹20 (b) ₹15 (c) ₹135 (d) ₹39
  9. 9.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹175 (c) ₹140 (d) ₹35
  10. 10.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 48 days (b) 3 days (c) 6 days (d) 18 days
  11. 11.If 3 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹120 (b) ₹108 (c) ₹42 (d) ₹324
  12. 12.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 27 days (d) 11 days
  13. 13.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹174 (d) ₹145
  14. 14.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
  15. 15.If 5 mangoes cost ₹40, how much do 2 mangoes cost? (a) ₹24 (b) ₹37 (c) ₹16 (d) ₹80
  16. 16.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 32 days (b) 33 days (c) 17 days (d) 7 days
  17. 17.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹31 (b) ₹186 (c) ₹155 (d) ₹217
  18. 18.If 2 kites cost ₹18, how much do 10 kites cost? (a) ₹99 (b) ₹26 (c) ₹90 (d) ₹180
  19. 19.5 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
  20. 20.If 9 kites cost ₹162, how much do 6 kites cost? (a) ₹126 (b) ₹108 (c) ₹159 (d) ₹972
  21. 21.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 30 days (d) 31 days
  22. 22.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹78 (b) ₹130 (c) ₹104 (d) ₹26
  23. 23.If 5 pens cost ₹35, how much do 6 pens cost? (a) ₹210 (b) ₹49 (c) ₹42 (d) ₹36
  24. 24.If 5 mangoes cost ₹40, how much do 4 mangoes cost? (a) ₹160 (b) ₹32 (c) ₹40 (d) ₹39
  25. 25.If 2 mangoes cost ₹28, how much do 7 mangoes cost? (a) ₹98 (b) ₹196 (c) ₹112 (d) ₹33
  26. 26.If 4 mangoes cost ₹96, how much do 5 mangoes cost? (a) ₹480 (b) ₹144 (c) ₹97 (d) ₹120
  27. 27.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹145 (b) ₹58 (c) ₹174 (d) ₹29
  28. 28.If 8 notebooks cost ₹96, how much do 7 notebooks cost? (a) ₹96 (b) ₹672 (c) ₹84 (d) ₹95
  29. 29.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹42 (d) ₹35
  30. 30.If 4 pens cost ₹64, how much do 6 pens cost? (a) ₹112 (b) ₹384 (c) ₹96 (d) ₹66
  31. 31.If 9 mangoes cost ₹153, how much do 12 mangoes cost? (a) ₹221 (b) ₹204 (c) ₹156 (d) ₹1836
  32. 32.If 3 mangoes cost ₹15, how much do 12 mangoes cost? (a) ₹65 (b) ₹180 (c) ₹24 (d) ₹60
  33. 33.4 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
  34. 34.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹165 (b) ₹99 (c) ₹33 (d) ₹231
  35. 35.If 2 pens cost ₹16, how much do 11 pens cost? (a) ₹88 (b) ₹96 (c) ₹25 (d) ₹176
  36. 36.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 4 days (d) 3 days
  37. 37.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 28 days (c) 13 days (d) 3 days
  38. 38.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹27 (d) ₹45
  39. 39.If 4 pens cost ₹44, how much do 3 pens cost? (a) ₹132 (b) ₹44 (c) ₹43 (d) ₹33
  40. 40.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 3 days (d) 12 days

Answer key

  1. 9 days
  2. 25 days
  3. ₹85
  4. ₹108
  5. 2 days
  6. ₹36
  7. ₹160
  8. ₹15
  9. ₹140
  10. 48 days
  11. ₹108
  12. 26 days
  13. ₹203
  14. 22 days
  15. ₹16
  16. 32 days
  17. ₹186
  18. ₹90
  19. 15 days
  20. ₹108
  21. 30 days
  22. ₹130
  23. ₹42
  24. ₹32
  25. ₹98
  26. ₹120
  27. ₹145
  28. ₹84
  29. ₹49
  30. ₹96
  31. ₹204
  32. ₹60
  33. 3 days
  34. ₹231
  35. ₹88
  36. 4 days
  37. 28 days
  38. ₹45
  39. ₹33
  40. 12 days

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