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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 499 · 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 4 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹20 (b) ₹128 (c) ₹32 (d) ₹36
  2. 2.If 8 mangoes cost ₹176, how much do 2 mangoes cost? (a) ₹170 (b) ₹66 (c) ₹352 (d) ₹44
  3. 3.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 12 days (d) 17 days
  4. 4.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹143 (b) ₹26 (c) ₹156 (d) ₹130
  5. 5.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹148 (b) ₹37 (c) ₹296 (d) ₹259
  6. 6.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 11 days (c) 15 days (d) 16 days
  7. 7.If 7 notebooks cost ₹119, how much do 9 notebooks cost? (a) ₹170 (b) ₹1071 (c) ₹121 (d) ₹153
  8. 8.₹205 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹164 (b) ₹41 (c) ₹82 (d) ₹123
  9. 9.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹13 (b) ₹104 (c) ₹91 (d) ₹52
  10. 10.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹232 (b) ₹116 (c) ₹29 (d) ₹203
  11. 11.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹329 (b) ₹235 (c) ₹282 (d) ₹47
  12. 12.If 8 pens cost ₹64, how much do 4 pens cost? (a) ₹32 (b) ₹256 (c) ₹60 (d) ₹40
  13. 13.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 28 days (d) 7 days
  14. 14.If 5 kites cost ₹45, how much do 12 kites cost? (a) ₹52 (b) ₹540 (c) ₹108 (d) ₹117
  15. 15.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 15 days (d) 12 days
  16. 16.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 15 days
  17. 17.If 5 notebooks cost ₹85, how much do 2 notebooks cost? (a) ₹170 (b) ₹34 (c) ₹51 (d) ₹82
  18. 18.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 6 days (d) 8 days
  19. 19.If 2 notebooks cost ₹16, how much do 6 notebooks cost? (a) ₹56 (b) ₹48 (c) ₹20 (d) ₹96
  20. 20.If 7 pens cost ₹77, how much do 8 pens cost? (a) ₹616 (b) ₹88 (c) ₹78 (d) ₹99
  21. 21.If 4 kites cost ₹76, how much do 8 kites cost? (a) ₹152 (b) ₹171 (c) ₹80 (d) ₹608
  22. 22.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹336 (b) ₹42 (c) ₹273 (d) ₹210
  23. 23.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹192 (d) ₹144
  24. 24.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 13 days (d) 28 days
  25. 25.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹147 (b) ₹126 (c) ₹21 (d) ₹105
  26. 26.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹45 (c) ₹9 (d) ₹81
  27. 27.If 3 pens cost ₹9, how much do 6 pens cost? (a) ₹54 (b) ₹12 (c) ₹21 (d) ₹18
  28. 28.If 6 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹47 (b) ₹48 (c) ₹240 (d) ₹40
  29. 29.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 23 days (c) 22 days (d) 7 days
  30. 30.₹126 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹14 (d) ₹70
  31. 31.If 6 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹45 (b) ₹270 (c) ₹53 (d) ₹54
  32. 32.If 7 notebooks cost ₹49, how much do 11 notebooks cost? (a) ₹84 (b) ₹539 (c) ₹53 (d) ₹77
  33. 33.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 12 days (d) 13 days
  34. 34.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹312 (c) ₹384 (d) ₹48
  35. 35.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹128 (b) ₹16 (c) ₹72 (d) ₹144
  36. 36.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 10 days (d) 3 days
  37. 37.If 6 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹198 (b) ₹33 (c) ₹23 (d) ₹36
  38. 38.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹315 (d) ₹350
  39. 39.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 19 days (d) 28 days
  40. 40.If 3 notebooks cost ₹42, how much do 10 notebooks cost? (a) ₹49 (b) ₹420 (c) ₹140 (d) ₹154

Answer key

  1. ₹32
  2. ₹44
  3. 12 days
  4. ₹156
  5. ₹259
  6. 15 days
  7. ₹153
  8. ₹123
  9. ₹91
  10. ₹203
  11. ₹282
  12. ₹32
  13. 7 days
  14. ₹108
  15. 14 days
  16. 7 days
  17. ₹34
  18. 7 days
  19. ₹48
  20. ₹88
  21. ₹152
  22. ₹336
  23. ₹240
  24. 27 days
  25. ₹126
  26. ₹72
  27. ₹18
  28. ₹40
  29. 22 days
  30. ₹70
  31. ₹45
  32. ₹77
  33. 12 days
  34. ₹384
  35. ₹128
  36. 2 days
  37. ₹33
  38. ₹315
  39. 7 days
  40. ₹140

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