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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 183 · 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 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 23 days (c) 22 days (d) 9 days
  2. 2.If 4 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹224 (b) ₹56 (c) ₹35 (d) ₹64
  3. 3.If 2 kites cost ₹50, how much do 6 kites cost? (a) ₹54 (b) ₹150 (c) ₹300 (d) ₹175
  4. 4.If 3 mangoes cost ₹21, how much do 2 mangoes cost? (a) ₹21 (b) ₹20 (c) ₹42 (d) ₹14
  5. 5.If 7 pens cost ₹133, how much do 8 pens cost? (a) ₹171 (b) ₹134 (c) ₹1064 (d) ₹152
  6. 6.If 7 mangoes cost ₹175, how much do 3 mangoes cost? (a) ₹171 (b) ₹100 (c) ₹525 (d) ₹75
  7. 7.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 20 days (d) 5 days
  8. 8.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹140 (b) ₹40 (c) ₹160 (d) ₹120
  9. 9.If 5 pens cost ₹15, how much do 7 pens cost? (a) ₹105 (b) ₹17 (c) ₹21 (d) ₹24
  10. 10.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹258 (b) ₹301 (c) ₹43 (d) ₹215
  11. 11.If 3 pens cost ₹12, how much do 7 pens cost? (a) ₹16 (b) ₹32 (c) ₹28 (d) ₹84
  12. 12.If 7 kites cost ₹35, how much do 3 kites cost? (a) ₹105 (b) ₹31 (c) ₹15 (d) ₹20
  13. 13.If 5 mangoes cost ₹30, how much do 2 mangoes cost? (a) ₹27 (b) ₹60 (c) ₹12 (d) ₹18
  14. 14.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 7 days (d) 3 days
  15. 15.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 3 days
  16. 16.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹42 (b) ₹126 (c) ₹210 (d) ₹252
  17. 17.If 5 kites cost ₹20, how much do 11 kites cost? (a) ₹220 (b) ₹26 (c) ₹48 (d) ₹44
  18. 18.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 63 days (d) 64 days
  19. 19.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 1 day (d) 3 days
  20. 20.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 12 days (d) 9 days
  21. 21.₹507 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹351 (b) ₹39 (c) ₹312 (d) ₹195
  22. 22.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 11 days (d) 4 days
  23. 23.If 4 kites cost ₹96, how much do 3 kites cost? (a) ₹95 (b) ₹96 (c) ₹72 (d) ₹288
  24. 24.₹315 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹280 (b) ₹35 (c) ₹281 (d) ₹315
  25. 25.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 5 days (d) 15 days
  26. 26.If 3 mangoes cost ₹66, how much do 6 mangoes cost? (a) ₹69 (b) ₹154 (c) ₹132 (d) ₹396
  27. 27.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 19 days (c) 11 days (d) 35 days
  28. 28.If 4 kites cost ₹100, how much do 7 kites cost? (a) ₹103 (b) ₹175 (c) ₹700 (d) ₹200
  29. 29.8 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
  30. 30.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹30 (b) ₹60 (c) ₹15 (d) ₹45
  31. 31.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹144 (b) ₹288 (c) ₹48 (d) ₹240
  32. 32.If 6 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹192 (b) ₹26 (c) ₹32 (d) ₹36
  33. 33.If 4 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹90 (b) ₹360 (c) ₹73 (d) ₹108
  34. 34.If 2 notebooks cost ₹32, how much do 3 notebooks cost? (a) ₹48 (b) ₹64 (c) ₹96 (d) ₹33
  35. 35.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 5 days (d) 33 days
  36. 36.If 2 notebooks cost ₹6, how much do 8 notebooks cost? (a) ₹27 (b) ₹12 (c) ₹48 (d) ₹24
  37. 37.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 5 days (d) 4 days
  38. 38.₹104 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹40 (b) ₹52 (c) ₹64 (d) ₹8
  39. 39.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹47 (b) ₹376 (c) ₹94 (d) ₹329
  40. 40.If 9 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹52 (b) ₹48 (c) ₹42 (d) ₹378

Answer key

  1. 22 days
  2. ₹56
  3. ₹150
  4. ₹14
  5. ₹152
  6. ₹75
  7. 20 days
  8. ₹160
  9. ₹21
  10. ₹301
  11. ₹28
  12. ₹15
  13. ₹12
  14. 10 days
  15. 7 days
  16. ₹210
  17. ₹44
  18. 63 days
  19. 3 days
  20. 12 days
  21. ₹312
  22. 10 days
  23. ₹72
  24. ₹280
  25. 35 days
  26. ₹132
  27. 35 days
  28. ₹175
  29. 32 days
  30. ₹45
  31. ₹240
  32. ₹32
  33. ₹90
  34. ₹48
  35. 33 days
  36. ₹24
  37. 4 days
  38. ₹64
  39. ₹329
  40. ₹42

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