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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 993 · 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.If 2 notebooks cost ₹8, how much do 3 notebooks cost? (a) ₹12 (b) ₹24 (c) ₹16 (d) ₹9
  2. 2.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
  3. 3.₹360 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹180 (b) ₹324 (c) ₹36 (d) ₹360
  4. 4.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 3 days (c) 17 days (d) 46 days
  5. 5.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
  6. 6.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹304 (b) ₹152 (c) ₹38 (d) ₹266
  7. 7.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 43 days (c) 42 days (d) 7 days
  8. 8.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹80 (b) ₹88 (c) ₹16 (d) ₹96
  9. 9.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 7 days (d) 8 days
  10. 10.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 4 days
  11. 11.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹169 (c) ₹26 (d) ₹104
  12. 12.If 5 mangoes cost ₹30, how much do 6 mangoes cost? (a) ₹31 (b) ₹180 (c) ₹42 (d) ₹36
  13. 13.If 2 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹120 (b) ₹24 (c) ₹70 (d) ₹60
  14. 14.₹190 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹133 (b) ₹95 (c) ₹57 (d) ₹19
  15. 15.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹30 (d) ₹40
  16. 16.₹282 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹141 (b) ₹235 (c) ₹47 (d) ₹282
  17. 17.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹70 (d) ₹40
  18. 18.If 7 notebooks cost ₹42, how much do 5 notebooks cost? (a) ₹30 (b) ₹210 (c) ₹40 (d) ₹36
  19. 19.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹15 (b) ₹90 (c) ₹105 (d) ₹91
  20. 20.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹6 (b) ₹39 (c) ₹24 (d) ₹54
  21. 21.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹120 (b) ₹15 (c) ₹135 (d) ₹45
  22. 22.If 8 notebooks cost ₹160, how much do 3 notebooks cost? (a) ₹480 (b) ₹60 (c) ₹155 (d) ₹80
  23. 23.If 6 kites cost ₹30, how much do 9 kites cost? (a) ₹45 (b) ₹50 (c) ₹270 (d) ₹33
  24. 24.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹15 (b) ₹48 (c) ₹16 (d) ₹12
  25. 25.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 14 days (d) 9 days
  26. 26.If 7 mangoes cost ₹91, how much do 8 mangoes cost? (a) ₹92 (b) ₹728 (c) ₹104 (d) ₹117
  27. 27.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 5 days (d) 6 days
  28. 28.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 2 days
  29. 29.If 4 kites cost ₹12, how much do 3 kites cost? (a) ₹11 (b) ₹36 (c) ₹12 (d) ₹9
  30. 30.If 8 kites cost ₹192, how much do 11 kites cost? (a) ₹2112 (b) ₹288 (c) ₹264 (d) ₹195
  31. 31.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 8 days
  32. 32.If 8 pens cost ₹64, how much do 9 pens cost? (a) ₹65 (b) ₹576 (c) ₹72 (d) ₹80
  33. 33.If 8 pens cost ₹56, how much do 6 pens cost? (a) ₹54 (b) ₹336 (c) ₹42 (d) ₹49
  34. 34.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 18 days (d) 19 days
  35. 35.If 6 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹24 (b) ₹19 (c) ₹126 (d) ₹21
  36. 36.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 15 days
  37. 37.If 2 notebooks cost ₹46, how much do 4 notebooks cost? (a) ₹184 (b) ₹92 (c) ₹115 (d) ₹48
  38. 38.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 24 days (d) 6 days
  39. 39.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 9 days (d) 8 days
  40. 40.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 41 days (b) 40 days (c) 20 days (d) 10 days

Answer key

  1. ₹12
  2. 3 days
  3. ₹324
  4. 45 days
  5. 45 days
  6. ₹266
  7. 42 days
  8. ₹96
  9. 7 days
  10. 4 days
  11. ₹234
  12. ₹36
  13. ₹60
  14. ₹133
  15. ₹50
  16. ₹235
  17. ₹100
  18. ₹30
  19. ₹90
  20. ₹54
  21. ₹120
  22. ₹60
  23. ₹45
  24. ₹12
  25. 14 days
  26. ₹104
  27. 7 days
  28. 8 days
  29. ₹9
  30. ₹264
  31. 9 days
  32. ₹72
  33. ₹42
  34. 18 days
  35. ₹21
  36. 21 days
  37. ₹92
  38. 6 days
  39. 9 days
  40. 40 days

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