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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 536 · 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. 1.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 17 days (d) 28 days
  2. 2.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹180 (b) ₹36 (c) ₹288 (d) ₹234
  3. 3.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 35 days (c) 15 days (d) 36 days
  4. 4.If 8 pens cost ₹48, how much do 2 pens cost? (a) ₹12 (b) ₹96 (c) ₹18 (d) ₹42
  5. 5.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹145 (d) ₹174
  6. 6.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹205 (d) ₹164
  7. 7.If 8 notebooks cost ₹32, how much do 2 notebooks cost? (a) ₹12 (b) ₹8 (c) ₹26 (d) ₹64
  8. 8.If 7 pens cost ₹98, how much do 6 pens cost? (a) ₹97 (b) ₹588 (c) ₹98 (d) ₹84
  9. 9.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 11 days (c) 21 days (d) 19 days
  10. 10.If 5 kites cost ₹95, how much do 7 kites cost? (a) ₹133 (b) ₹152 (c) ₹665 (d) ₹97
  11. 11.If 9 kites cost ₹117, how much do 7 kites cost? (a) ₹91 (b) ₹104 (c) ₹115 (d) ₹819
  12. 12.If 3 kites cost ₹27, how much do 7 kites cost? (a) ₹189 (b) ₹72 (c) ₹63 (d) ₹31
  13. 13.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 7 days (d) 17 days
  14. 14.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹153 (d) ₹136
  15. 15.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 10 days (c) 27 days (d) 16 days
  16. 16.If 7 pens cost ₹175, how much do 10 pens cost? (a) ₹1750 (b) ₹178 (c) ₹275 (d) ₹250
  17. 17.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 5 days (d) 45 days
  18. 18.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 13 days (d) 27 days
  19. 19.If 5 pens cost ₹45, how much do 6 pens cost? (a) ₹46 (b) ₹63 (c) ₹270 (d) ₹54
  20. 20.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 6 days (d) 7 days
  21. 21.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 35 days (c) 36 days (d) 11 days
  22. 22.If 8 mangoes cost ₹120, how much do 6 mangoes cost? (a) ₹118 (b) ₹105 (c) ₹720 (d) ₹90
  23. 23.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 7 days (d) 6 days
  24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
  25. 25.If 9 pens cost ₹45, how much do 11 pens cost? (a) ₹60 (b) ₹47 (c) ₹55 (d) ₹495
  26. 26.If 6 kites cost ₹78, how much do 10 kites cost? (a) ₹780 (b) ₹82 (c) ₹143 (d) ₹130
  27. 27.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 15 days (d) 6 days
  28. 28.If 4 pens cost ₹20, how much do 5 pens cost? (a) ₹100 (b) ₹21 (c) ₹30 (d) ₹25
  29. 29.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 12 days (d) 13 days
  30. 30.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 14 days (c) 16 days (d) 15 days
  31. 31.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹245 (b) ₹49 (c) ₹392 (d) ₹441
  32. 32.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹36 (b) ₹13 (c) ₹18 (d) ₹24
  33. 33.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 2 days (d) 13 days
  34. 34.If 2 pens cost ₹42, how much do 6 pens cost? (a) ₹46 (b) ₹126 (c) ₹252 (d) ₹147
  35. 35.If 6 pens cost ₹120, how much do 7 pens cost? (a) ₹160 (b) ₹840 (c) ₹140 (d) ₹121
  36. 36.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 16 days (d) 1 day
  37. 37.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 21 days (d) 17 days
  38. 38.₹66 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹54 (b) ₹12 (c) ₹33 (d) ₹6
  39. 39.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹230 (b) ₹184 (c) ₹138 (d) ₹46
  40. 40.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 48 days (b) 18 days (c) 6 days (d) 3 days

Answer key

  1. 7 days
  2. ₹288
  3. 35 days
  4. ₹12
  5. ₹145
  6. ₹205
  7. ₹8
  8. ₹84
  9. 20 days
  10. ₹133
  11. ₹91
  12. ₹63
  13. 16 days
  14. ₹136
  15. 26 days
  16. ₹250
  17. 45 days
  18. 27 days
  19. ₹54
  20. 6 days
  21. 35 days
  22. ₹90
  23. 6 days
  24. 9 days
  25. ₹55
  26. ₹130
  27. 7 days
  28. ₹25
  29. 12 days
  30. 15 days
  31. ₹392
  32. ₹18
  33. 1 day
  34. ₹126
  35. ₹140
  36. 16 days
  37. 21 days
  38. ₹54
  39. ₹230
  40. 48 days

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