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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 227 · 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 4 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 17 days (c) 11 days (d) 19 days
  2. 2.If 3 mangoes cost ₹24, how much do 7 mangoes cost? (a) ₹28 (b) ₹56 (c) ₹168 (d) ₹64
  3. 3.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹65 (b) ₹26 (c) ₹13 (d) ₹78
  4. 4.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹49 (d) ₹42
  5. 5.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹333 (b) ₹296 (c) ₹111 (d) ₹37
  6. 6.If 3 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹198 (b) ₹61 (c) ₹180 (d) ₹540
  7. 7.If 4 pens cost ₹56, how much do 3 pens cost? (a) ₹56 (b) ₹55 (c) ₹42 (d) ₹168
  8. 8.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 4 days (d) 3 days
  9. 9.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 13 days (c) 16 days (d) 1 day
  10. 10.If 4 pens cost ₹76, how much do 9 pens cost? (a) ₹190 (b) ₹81 (c) ₹684 (d) ₹171
  11. 11.If 3 pens cost ₹66, how much do 7 pens cost? (a) ₹70 (b) ₹462 (c) ₹176 (d) ₹154
  12. 12.If 9 mangoes cost ₹117, how much do 11 mangoes cost? (a) ₹119 (b) ₹1287 (c) ₹156 (d) ₹143
  13. 13.₹170 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹170 (b) ₹85 (c) ₹34 (d) ₹136
  14. 14.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 1 day (d) 22 days
  15. 15.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 45 days (d) 21 days
  16. 16.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹216 (d) ₹240
  17. 17.If 5 notebooks cost ₹100, how much do 4 notebooks cost? (a) ₹400 (b) ₹99 (c) ₹100 (d) ₹80
  18. 18.If 8 pens cost ₹40, how much do 3 pens cost? (a) ₹35 (b) ₹20 (c) ₹120 (d) ₹15
  19. 19.If 5 notebooks cost ₹35, how much do 2 notebooks cost? (a) ₹32 (b) ₹14 (c) ₹21 (d) ₹70
  20. 20.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹68 (d) ₹34
  21. 21.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 11 days (d) 15 days
  22. 22.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹105 (b) ₹90 (c) ₹15 (d) ₹75
  23. 23.₹147 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹49 (b) ₹99 (c) ₹98 (d) ₹147
  24. 24.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 3 days (d) 4 days
  25. 25.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 19 days (d) 28 days
  26. 26.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹180 (b) ₹450 (c) ₹405 (d) ₹45
  27. 27.If 7 notebooks cost ₹112, how much do 10 notebooks cost? (a) ₹115 (b) ₹176 (c) ₹1120 (d) ₹160
  28. 28.3 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
  29. 29.If 3 pens cost ₹66, how much do 4 pens cost? (a) ₹88 (b) ₹67 (c) ₹110 (d) ₹264
  30. 30.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 27 days (d) 3 days
  31. 31.₹54 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹6 (b) ₹42 (c) ₹12 (d) ₹27
  32. 32.If 2 pens cost ₹26, how much do 6 pens cost? (a) ₹78 (b) ₹30 (c) ₹91 (d) ₹156
  33. 33.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹144 (d) ₹128
  34. 34.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
  35. 35.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹18 (d) ₹99
  36. 36.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 12 days (d) 3 days
  37. 37.If 3 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹234 (b) ₹648 (c) ₹63 (d) ₹216
  38. 38.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 11 days (d) 5 days
  39. 39.₹72 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹27 (c) ₹9 (d) ₹45
  40. 40.If 8 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹576 (b) ₹78 (c) ₹72 (d) ₹52

Answer key

  1. 18 days
  2. ₹56
  3. ₹65
  4. ₹42
  5. ₹296
  6. ₹180
  7. ₹42
  8. 4 days
  9. 1 day
  10. ₹171
  11. ₹154
  12. ₹143
  13. ₹136
  14. 21 days
  15. 45 days
  16. ₹240
  17. ₹80
  18. ₹15
  19. ₹14
  20. ₹51
  21. 26 days
  22. ₹90
  23. ₹98
  24. 4 days
  25. 27 days
  26. ₹405
  27. ₹160
  28. 21 days
  29. ₹88
  30. 27 days
  31. ₹42
  32. ₹78
  33. ₹160
  34. 3 days
  35. ₹162
  36. 12 days
  37. ₹216
  38. 6 days
  39. ₹45
  40. ₹72

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