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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 381 · 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 6 pens cost ₹102, how much do 2 pens cost? (a) ₹204 (b) ₹34 (c) ₹51 (d) ₹98
  2. 2.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹90 (d) ₹75
  3. 3.If 7 mangoes cost ₹77, how much do 9 mangoes cost? (a) ₹110 (b) ₹99 (c) ₹79 (d) ₹693
  4. 4.If 9 mangoes cost ₹126, how much do 4 mangoes cost? (a) ₹121 (b) ₹56 (c) ₹504 (d) ₹70
  5. 5.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹99 (d) ₹18
  6. 6.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 18 days (d) 19 days
  7. 7.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹196 (b) ₹147 (c) ₹49 (d) ₹245
  8. 8.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹90 (c) ₹18 (d) ₹144
  9. 9.₹288 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹288 (d) ₹144
  10. 10.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 52 days (d) 7 days
  11. 11.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹196 (c) ₹245 (d) ₹49
  12. 12.If 6 pens cost ₹138, how much do 2 pens cost? (a) ₹276 (b) ₹69 (c) ₹134 (d) ₹46
  13. 13.If 3 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹594 (b) ₹198 (c) ₹62 (d) ₹216
  14. 14.If 3 kites cost ₹21, how much do 8 kites cost? (a) ₹63 (b) ₹56 (c) ₹168 (d) ₹26
  15. 15.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹23 (b) ₹11 (c) ₹33 (d) ₹22
  16. 16.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 30 days (c) 17 days (d) 13 days
  17. 17.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹36 (b) ₹42 (c) ₹12 (d) ₹48
  18. 18.If 5 kites cost ₹100, how much do 2 kites cost? (a) ₹97 (b) ₹200 (c) ₹60 (d) ₹40
  19. 19.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹315 (c) ₹350 (d) ₹35
  20. 20.If 9 kites cost ₹180, how much do 8 kites cost? (a) ₹180 (b) ₹160 (c) ₹1440 (d) ₹179
  21. 21.If 7 notebooks cost ₹42, how much do 6 notebooks cost? (a) ₹42 (b) ₹41 (c) ₹252 (d) ₹36
  22. 22.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹48 (b) ₹432 (c) ₹240 (d) ₹336
  23. 23.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  24. 24.If 2 pens cost ₹38, how much do 3 pens cost? (a) ₹39 (b) ₹114 (c) ₹57 (d) ₹76
  25. 25.If 7 pens cost ₹175, how much do 2 pens cost? (a) ₹75 (b) ₹50 (c) ₹350 (d) ₹170
  26. 26.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 2 days (d) 7 days
  27. 27.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 14 days (d) 22 days
  28. 28.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 17 days (d) 7 days
  29. 29.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹24 (d) ₹6
  30. 30.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 15 days (d) 6 days
  31. 31.If 2 mangoes cost ₹12, how much do 3 mangoes cost? (a) ₹36 (b) ₹18 (c) ₹13 (d) ₹24
  32. 32.If 3 notebooks cost ₹33, how much do 2 notebooks cost? (a) ₹33 (b) ₹32 (c) ₹66 (d) ₹22
  33. 33.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 16 days (d) 4 days
  34. 34.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 15 days
  35. 35.If 5 kites cost ₹60, how much do 11 kites cost? (a) ₹660 (b) ₹144 (c) ₹66 (d) ₹132
  36. 36.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹112 (d) ₹126
  37. 37.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹280 (d) ₹360
  38. 38.If 7 notebooks cost ₹35, how much do 10 notebooks cost? (a) ₹55 (b) ₹350 (c) ₹50 (d) ₹38
  39. 39.If 5 mangoes cost ₹50, how much do 4 mangoes cost? (a) ₹40 (b) ₹49 (c) ₹200 (d) ₹50
  40. 40.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days

Answer key

  1. ₹34
  2. ₹105
  3. ₹99
  4. ₹56
  5. ₹162
  6. 18 days
  7. ₹245
  8. ₹144
  9. ₹240
  10. 52 days
  11. ₹196
  12. ₹46
  13. ₹198
  14. ₹56
  15. ₹22
  16. 30 days
  17. ₹48
  18. ₹40
  19. ₹315
  20. ₹160
  21. ₹36
  22. ₹432
  23. 25 days
  24. ₹57
  25. ₹50
  26. 8 days
  27. 22 days
  28. 42 days
  29. ₹18
  30. 6 days
  31. ₹18
  32. ₹22
  33. 16 days
  34. 12 days
  35. ₹132
  36. ₹140
  37. ₹360
  38. ₹50
  39. ₹40
  40. 2 days

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