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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 419 · 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.₹384 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹384 (b) ₹192 (c) ₹336 (d) ₹48
  2. 2.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹66 (d) ₹88
  3. 3.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 36 days (d) 6 days
  4. 4.If 2 notebooks cost ₹50, how much do 8 notebooks cost? (a) ₹200 (b) ₹56 (c) ₹400 (d) ₹225
  5. 5.If 2 kites cost ₹6, how much do 3 kites cost? (a) ₹12 (b) ₹7 (c) ₹18 (d) ₹9
  6. 6.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 19 days (c) 11 days (d) 18 days
  7. 7.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 33 days (d) 17 days
  8. 8.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹11 (d) ₹77
  9. 9.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 5 days (d) 4 days
  10. 10.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
  11. 11.If 2 kites cost ₹10, how much do 11 kites cost? (a) ₹110 (b) ₹60 (c) ₹19 (d) ₹55
  12. 12.If 3 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹84 (b) ₹28 (c) ₹22 (d) ₹35
  13. 13.If 3 pens cost ₹60, how much do 2 pens cost? (a) ₹40 (b) ₹60 (c) ₹59 (d) ₹120
  14. 14.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹108 (d) ₹90
  15. 15.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹405 (d) ₹225
  16. 16.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹34 (b) ₹238 (c) ₹102 (d) ₹170
  17. 17.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹37 (b) ₹111 (c) ₹148 (d) ₹185
  18. 18.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 19 days (d) 11 days
  19. 19.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days
  20. 20.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹192 (b) ₹144 (c) ₹48 (d) ₹240
  21. 21.If 9 notebooks cost ₹180, how much do 3 notebooks cost? (a) ₹540 (b) ₹80 (c) ₹174 (d) ₹60
  22. 22.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 17 days (d) 9 days
  23. 23.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹21 (b) ₹147 (c) ₹126 (d) ₹105
  24. 24.If 3 kites cost ₹36, how much do 6 kites cost? (a) ₹84 (b) ₹72 (c) ₹39 (d) ₹216
  25. 25.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹8 (c) ₹36 (d) ₹64
  26. 26.If 4 pens cost ₹28, how much do 6 pens cost? (a) ₹49 (b) ₹42 (c) ₹30 (d) ₹168
  27. 27.If 2 mangoes cost ₹22, how much do 12 mangoes cost? (a) ₹32 (b) ₹264 (c) ₹143 (d) ₹132
  28. 28.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 9 days
  29. 29.If 2 mangoes cost ₹18, how much do 3 mangoes cost? (a) ₹54 (b) ₹27 (c) ₹19 (d) ₹36
  30. 30.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹155 (d) ₹217
  31. 31.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹16 (b) ₹25 (c) ₹60 (d) ₹20
  32. 32.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹128 (b) ₹16 (c) ₹48 (d) ₹88
  33. 33.If 8 pens cost ₹112, how much do 9 pens cost? (a) ₹140 (b) ₹1008 (c) ₹113 (d) ₹126
  34. 34.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 14 days
  35. 35.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹63 (b) ₹81 (c) ₹9 (d) ₹45
  36. 36.If 5 mangoes cost ₹100, how much do 9 mangoes cost? (a) ₹200 (b) ₹104 (c) ₹180 (d) ₹900
  37. 37.If 7 notebooks cost ₹42, how much do 2 notebooks cost? (a) ₹18 (b) ₹84 (c) ₹12 (d) ₹37
  38. 38.If 2 mangoes cost ₹16, how much do 6 mangoes cost? (a) ₹96 (b) ₹48 (c) ₹20 (d) ₹56
  39. 39.If 5 pens cost ₹25, how much do 7 pens cost? (a) ₹40 (b) ₹35 (c) ₹27 (d) ₹175
  40. 40.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹66 (d) ₹77

Answer key

  1. ₹336
  2. ₹88
  3. 4 days
  4. ₹200
  5. ₹9
  6. 18 days
  7. 33 days
  8. ₹77
  9. 4 days
  10. 7 days
  11. ₹55
  12. ₹28
  13. ₹40
  14. ₹90
  15. ₹405
  16. ₹238
  17. ₹148
  18. 35 days
  19. 27 days
  20. ₹240
  21. ₹60
  22. 9 days
  23. ₹147
  24. ₹72
  25. ₹64
  26. ₹42
  27. ₹132
  28. 8 days
  29. ₹27
  30. ₹217
  31. ₹20
  32. ₹128
  33. ₹126
  34. 8 days
  35. ₹81
  36. ₹180
  37. ₹12
  38. ₹48
  39. ₹35
  40. ₹88

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