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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 867 · 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 9 notebooks cost ₹225, how much do 8 notebooks cost? (a) ₹200 (b) ₹225 (c) ₹1800 (d) ₹224
  2. 2.If 2 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹37 (b) ₹112 (c) ₹128 (d) ₹224
  3. 3.If 3 mangoes cost ₹12, how much do 4 mangoes cost? (a) ₹13 (b) ₹16 (c) ₹48 (d) ₹20
  4. 4.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹77 (c) ₹11 (d) ₹66
  5. 5.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 49 days (d) 4 days
  6. 6.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹58 (b) ₹29 (c) ₹116 (d) ₹87
  7. 7.If 5 mangoes cost ₹30, how much do 8 mangoes cost? (a) ₹48 (b) ₹33 (c) ₹54 (d) ₹240
  8. 8.If 9 notebooks cost ₹144, how much do 7 notebooks cost? (a) ₹128 (b) ₹142 (c) ₹1008 (d) ₹112
  9. 9.If 5 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹360 (b) ₹72 (c) ₹80 (d) ₹44
  10. 10.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 28 days (d) 11 days
  11. 11.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹117 (d) ₹130
  12. 12.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 5 days (d) 8 days
  13. 13.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 1 day
  14. 14.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 18 days (d) 13 days
  15. 15.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹85 (d) ₹119
  16. 16.If 6 pens cost ₹54, how much do 11 pens cost? (a) ₹594 (b) ₹108 (c) ₹99 (d) ₹59
  17. 17.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 7 days (d) 6 days
  18. 18.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹37 (b) ₹222 (c) ₹185 (d) ₹259
  19. 19.If 3 notebooks cost ₹63, how much do 11 notebooks cost? (a) ₹231 (b) ₹693 (c) ₹71 (d) ₹252
  20. 20.If 9 kites cost ₹36, how much do 8 kites cost? (a) ₹32 (b) ₹36 (c) ₹288 (d) ₹35
  21. 21.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹16 (d) ₹48
  22. 22.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹85 (c) ₹17 (d) ₹119
  23. 23.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹72 (d) ₹64
  24. 24.If 9 pens cost ₹135, how much do 8 pens cost? (a) ₹135 (b) ₹120 (c) ₹134 (d) ₹1080
  25. 25.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 40 days (c) 16 days (d) 41 days
  26. 26.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹130 (b) ₹20 (c) ₹80 (d) ₹180
  27. 27.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 18 days (b) 28 days (c) 7 days (d) 10 days
  28. 28.If 6 kites cost ₹66, how much do 7 kites cost? (a) ₹88 (b) ₹462 (c) ₹67 (d) ₹77
  29. 29.If 9 pens cost ₹36, how much do 8 pens cost? (a) ₹35 (b) ₹32 (c) ₹36 (d) ₹288
  30. 30.₹442 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹34 (b) ₹221 (c) ₹272 (d) ₹170
  31. 31.If 2 pens cost ₹40, how much do 3 pens cost? (a) ₹120 (b) ₹80 (c) ₹41 (d) ₹60
  32. 32.If 6 pens cost ₹114, how much do 2 pens cost? (a) ₹228 (b) ₹57 (c) ₹110 (d) ₹38
  33. 33.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹126 (b) ₹336 (c) ₹231 (d) ₹42
  34. 34.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹198 (b) ₹165 (c) ₹231 (d) ₹33
  35. 35.If 5 kites cost ₹75, how much do 4 kites cost? (a) ₹75 (b) ₹74 (c) ₹60 (d) ₹300
  36. 36.₹266 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹38 (b) ₹152 (c) ₹133 (d) ₹114
  37. 37.If 6 kites cost ₹72, how much do 8 kites cost? (a) ₹96 (b) ₹576 (c) ₹108 (d) ₹74
  38. 38.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 9 days (d) 26 days
  39. 39.If 4 kites cost ₹68, how much do 9 kites cost? (a) ₹612 (b) ₹153 (c) ₹73 (d) ₹170
  40. 40.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹30 (d) ₹10

Answer key

  1. ₹200
  2. ₹112
  3. ₹16
  4. ₹66
  5. 49 days
  6. ₹87
  7. ₹48
  8. ₹112
  9. ₹72
  10. 7 days
  11. ₹130
  12. 8 days
  13. 21 days
  14. 18 days
  15. ₹153
  16. ₹99
  17. 7 days
  18. ₹222
  19. ₹231
  20. ₹32
  21. ₹48
  22. ₹119
  23. ₹80
  24. ₹120
  25. 40 days
  26. ₹180
  27. 7 days
  28. ₹77
  29. ₹32
  30. ₹272
  31. ₹60
  32. ₹38
  33. ₹336
  34. ₹231
  35. ₹60
  36. ₹152
  37. ₹96
  38. 26 days
  39. ₹153
  40. ₹20

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