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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 329 · 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. 1.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 32 days (d) 14 days
  2. 2.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 14 days (d) 15 days
  3. 3.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 16 days (d) 4 days
  4. 4.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹29 (b) ₹59 (c) ₹58 (d) ₹87
  5. 5.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 6 days (d) 7 days
  6. 6.If 5 notebooks cost ₹105, how much do 6 notebooks cost? (a) ₹126 (b) ₹630 (c) ₹106 (d) ₹147
  7. 7.If 4 kites cost ₹96, how much do 5 kites cost? (a) ₹480 (b) ₹120 (c) ₹97 (d) ₹144
  8. 8.If 6 pens cost ₹18, how much do 2 pens cost? (a) ₹36 (b) ₹6 (c) ₹14 (d) ₹9
  9. 9.If 7 notebooks cost ₹175, how much do 10 notebooks cost? (a) ₹275 (b) ₹1750 (c) ₹178 (d) ₹250
  10. 10.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 20 days (d) 21 days
  11. 11.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹68 (b) ₹51 (c) ₹17 (d) ₹85
  12. 12.If 4 kites cost ₹88, how much do 3 kites cost? (a) ₹88 (b) ₹66 (c) ₹87 (d) ₹264
  13. 13.If 2 pens cost ₹18, how much do 3 pens cost? (a) ₹54 (b) ₹19 (c) ₹27 (d) ₹36
  14. 14.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹40 (d) ₹80
  15. 15.If 6 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹92 (b) ₹48 (c) ₹32 (d) ₹192
  16. 16.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹144 (b) ₹112 (c) ₹80 (d) ₹16
  17. 17.If 6 kites cost ₹126, how much do 5 kites cost? (a) ₹125 (b) ₹126 (c) ₹630 (d) ₹105
  18. 18.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹294 (d) ₹343
  19. 19.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹60 (c) ₹20 (d) ₹80
  20. 20.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 11 days (d) 8 days
  21. 21.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 8 days (d) 3 days
  22. 22.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹42 (b) ₹252 (c) ₹48 (d) ₹37
  23. 23.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 10 days (d) 8 days
  24. 24.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 15 days (d) 21 days
  25. 25.If 5 pens cost ₹110, how much do 7 pens cost? (a) ₹176 (b) ₹154 (c) ₹770 (d) ₹112
  26. 26.If 2 pens cost ₹6, how much do 4 pens cost? (a) ₹15 (b) ₹24 (c) ₹12 (d) ₹8
  27. 27.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 5 days (d) 4 days
  28. 28.₹301 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹43 (b) ₹259 (c) ₹301 (d) ₹258
  29. 29.If 8 notebooks cost ₹160, how much do 12 notebooks cost? (a) ₹240 (b) ₹260 (c) ₹164 (d) ₹1920
  30. 30.If 8 kites cost ₹176, how much do 7 kites cost? (a) ₹1232 (b) ₹154 (c) ₹176 (d) ₹175
  31. 31.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 2 days (d) 32 days
  32. 32.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹124 (b) ₹93 (c) ₹155 (d) ₹31
  33. 33.If 4 pens cost ₹24, how much do 11 pens cost? (a) ₹264 (b) ₹72 (c) ₹66 (d) ₹31
  34. 34.If 2 kites cost ₹10, how much do 4 kites cost? (a) ₹12 (b) ₹40 (c) ₹20 (d) ₹25
  35. 35.If 4 kites cost ₹36, how much do 5 kites cost? (a) ₹180 (b) ₹54 (c) ₹37 (d) ₹45
  36. 36.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 1 day (d) 17 days
  37. 37.If 5 pens cost ₹105, how much do 6 pens cost? (a) ₹126 (b) ₹630 (c) ₹106 (d) ₹147
  38. 38.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 11 days (d) 16 days
  39. 39.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 8 days (d) 18 days
  40. 40.If 3 mangoes cost ₹42, how much do 9 mangoes cost? (a) ₹48 (b) ₹126 (c) ₹140 (d) ₹378

Answer key

  1. 32 days
  2. 14 days
  3. 4 days
  4. ₹58
  5. 7 days
  6. ₹126
  7. ₹120
  8. ₹6
  9. ₹250
  10. 20 days
  11. ₹85
  12. ₹66
  13. ₹27
  14. ₹70
  15. ₹32
  16. ₹144
  17. ₹105
  18. ₹343
  19. ₹60
  20. 8 days
  21. 2 days
  22. ₹42
  23. 8 days
  24. 21 days
  25. ₹154
  26. ₹12
  27. 16 days
  28. ₹258
  29. ₹240
  30. ₹154
  31. 2 days
  32. ₹124
  33. ₹66
  34. ₹20
  35. ₹45
  36. 16 days
  37. ₹126
  38. 15 days
  39. 18 days
  40. ₹126

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