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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 489 · 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 5 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 15 days (d) 11 days
  2. 2.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹225 (b) ₹315 (c) ₹45 (d) ₹405
  3. 3.If 7 notebooks cost ₹140, how much do 8 notebooks cost? (a) ₹160 (b) ₹1120 (c) ₹141 (d) ₹180
  4. 4.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹205 (d) ₹328
  5. 5.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 5 days (d) 6 days
  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) 15 days (d) 27 days
  7. 7.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹36 (d) ₹40
  8. 8.If 8 kites cost ₹120, how much do 5 kites cost? (a) ₹600 (b) ₹75 (c) ₹90 (d) ₹117
  9. 9.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹16 (c) ₹128 (d) ₹144
  10. 10.If 9 mangoes cost ₹126, how much do 10 mangoes cost? (a) ₹140 (b) ₹154 (c) ₹1260 (d) ₹127
  11. 11.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹114 (b) ₹190 (c) ₹228 (d) ₹38
  12. 12.If 8 kites cost ₹40, how much do 3 kites cost? (a) ₹20 (b) ₹35 (c) ₹120 (d) ₹15
  13. 13.If 9 kites cost ₹225, how much do 10 kites cost? (a) ₹2250 (b) ₹250 (c) ₹226 (d) ₹275
  14. 14.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹132 (b) ₹96 (c) ₹24 (d) ₹168
  15. 15.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹22 (d) ₹33
  16. 16.If 4 mangoes cost ₹56, how much do 5 mangoes cost? (a) ₹280 (b) ₹84 (c) ₹70 (d) ₹57
  17. 17.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 13 days (d) 9 days
  18. 18.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
  19. 19.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 5 days (d) 20 days
  20. 20.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 3 days (d) 11 days
  21. 21.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹49 (c) ₹14 (d) ₹70
  22. 22.If 6 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹72 (b) ₹18 (c) ₹32 (d) ₹12
  23. 23.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 28 days
  24. 24.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 11 days (d) 13 days
  25. 25.₹88 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹77 (b) ₹44 (c) ₹11 (d) ₹88
  26. 26.If 5 notebooks cost ₹105, how much do 2 notebooks cost? (a) ₹102 (b) ₹42 (c) ₹210 (d) ₹63
  27. 27.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 11 days (d) 26 days
  28. 28.If 5 mangoes cost ₹25, how much do 8 mangoes cost? (a) ₹45 (b) ₹28 (c) ₹40 (d) ₹200
  29. 29.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 10 days (d) 4 days
  30. 30.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 5 days (d) 20 days
  31. 31.If 8 mangoes cost ₹88, how much do 2 mangoes cost? (a) ₹22 (b) ₹176 (c) ₹33 (d) ₹82
  32. 32.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹32 (c) ₹256 (d) ₹208
  33. 33.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹115 (b) ₹46 (c) ₹92 (d) ₹138
  34. 34.If 2 kites cost ₹40, how much do 5 kites cost? (a) ₹200 (b) ₹120 (c) ₹43 (d) ₹100
  35. 35.If 7 pens cost ₹119, how much do 10 pens cost? (a) ₹187 (b) ₹122 (c) ₹1190 (d) ₹170
  36. 36.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹18 (c) ₹9 (d) ₹27
  37. 37.If 3 kites cost ₹57, how much do 9 kites cost? (a) ₹190 (b) ₹513 (c) ₹171 (d) ₹63
  38. 38.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹27 (b) ₹9 (c) ₹45 (d) ₹36
  39. 39.If 2 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹72 (b) ₹27 (c) ₹120 (d) ₹60
  40. 40.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 4 days (d) 5 days

Answer key

  1. 15 days
  2. ₹405
  3. ₹160
  4. ₹328
  5. 5 days
  6. 3 days
  7. ₹40
  8. ₹75
  9. ₹128
  10. ₹140
  11. ₹190
  12. ₹15
  13. ₹250
  14. ₹168
  15. ₹33
  16. ₹70
  17. 22 days
  18. 5 days
  19. 5 days
  20. 10 days
  21. ₹70
  22. ₹12
  23. 28 days
  24. 12 days
  25. ₹77
  26. ₹42
  27. 26 days
  28. ₹40
  29. 9 days
  30. 5 days
  31. ₹22
  32. ₹256
  33. ₹138
  34. ₹100
  35. ₹170
  36. ₹27
  37. ₹171
  38. ₹36
  39. ₹60
  40. 9 days

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