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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 882 · 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. 1.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 10 days (d) 7 days
  2. 2.If 8 kites cost ₹176, how much do 12 kites cost? (a) ₹286 (b) ₹180 (c) ₹264 (d) ₹2112
  3. 3.If 4 kites cost ₹32, how much do 10 kites cost? (a) ₹320 (b) ₹38 (c) ₹88 (d) ₹80
  4. 4.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 22 days (c) 21 days (d) 16 days
  5. 5.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹30 (b) ₹35 (c) ₹10 (d) ₹40
  6. 6.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 27 days (d) 15 days
  7. 7.₹266 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹133 (b) ₹76 (c) ₹38 (d) ₹190
  8. 8.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 9 days (c) 5 days (d) 21 days
  9. 9.If 9 pens cost ₹144, how much do 8 pens cost? (a) ₹143 (b) ₹144 (c) ₹128 (d) ₹1152
  10. 10.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹8 (b) ₹72 (c) ₹56 (d) ₹40
  11. 11.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹76 (b) ₹57 (c) ₹19 (d) ₹38
  12. 12.₹396 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹198 (b) ₹176 (c) ₹220 (d) ₹44
  13. 13.If 2 notebooks cost ₹26, how much do 10 notebooks cost? (a) ₹143 (b) ₹130 (c) ₹34 (d) ₹260
  14. 14.If 6 kites cost ₹96, how much do 3 kites cost? (a) ₹288 (b) ₹48 (c) ₹64 (d) ₹93
  15. 15.If 6 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹64 (b) ₹49 (c) ₹336 (d) ₹56
  16. 16.3 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) 7 days (d) 6 days
  17. 17.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹344 (b) ₹387 (c) ₹43 (d) ₹345
  18. 18.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹414 (b) ₹184 (c) ₹46 (d) ₹299
  19. 19.If 8 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹33 (b) ₹288 (c) ₹40 (d) ₹36
  20. 20.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹66 (b) ₹44 (c) ₹55 (d) ₹11
  21. 21.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 36 days (d) 19 days
  22. 22.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 52 days (c) 7 days (d) 19 days
  23. 23.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹12 (b) ₹54 (c) ₹96 (d) ₹108
  24. 24.If 5 pens cost ₹90, how much do 11 pens cost? (a) ₹216 (b) ₹198 (c) ₹990 (d) ₹96
  25. 25.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
  26. 26.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 27 days (d) 3 days
  27. 27.If 3 pens cost ₹66, how much do 2 pens cost? (a) ₹65 (b) ₹66 (c) ₹44 (d) ₹132
  28. 28.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 15 days
  29. 29.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 11 days (d) 7 days
  30. 30.If 3 kites cost ₹24, how much do 5 kites cost? (a) ₹120 (b) ₹48 (c) ₹26 (d) ₹40
  31. 31.If 6 mangoes cost ₹132, how much do 4 mangoes cost? (a) ₹88 (b) ₹110 (c) ₹528 (d) ₹130
  32. 32.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹145 (b) ₹117 (c) ₹29 (d) ₹116
  33. 33.If 5 pens cost ₹120, how much do 4 pens cost? (a) ₹96 (b) ₹480 (c) ₹120 (d) ₹119
  34. 34.If 2 pens cost ₹6, how much do 4 pens cost? (a) ₹8 (b) ₹15 (c) ₹12 (d) ₹24
  35. 35.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹60 (d) ₹54
  36. 36.If 3 kites cost ₹69, how much do 5 kites cost? (a) ₹115 (b) ₹345 (c) ₹71 (d) ₹138
  37. 37.If 9 kites cost ₹117, how much do 4 kites cost? (a) ₹468 (b) ₹65 (c) ₹52 (d) ₹112
  38. 38.₹200 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹20 (b) ₹100 (c) ₹60 (d) ₹140
  39. 39.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹165 (b) ₹30 (c) ₹60 (d) ₹270
  40. 40.If 5 pens cost ₹100, how much do 3 pens cost? (a) ₹300 (b) ₹98 (c) ₹80 (d) ₹60

Answer key

  1. 9 days
  2. ₹264
  3. ₹80
  4. 21 days
  5. ₹40
  6. 3 days
  7. ₹190
  8. 45 days
  9. ₹128
  10. ₹72
  11. ₹57
  12. ₹220
  13. ₹130
  14. ₹48
  15. ₹56
  16. 6 days
  17. ₹344
  18. ₹414
  19. ₹36
  20. ₹55
  21. 35 days
  22. 52 days
  23. ₹96
  24. ₹198
  25. 3 days
  26. 27 days
  27. ₹44
  28. 7 days
  29. 7 days
  30. ₹40
  31. ₹88
  32. ₹116
  33. ₹96
  34. ₹12
  35. ₹60
  36. ₹115
  37. ₹52
  38. ₹140
  39. ₹270
  40. ₹60

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