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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 938 · 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. 1.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 14 days (b) 7 days (c) 6 days (d) 5 days
  2. 2.If 2 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹264 (b) ₹33 (c) ₹132 (d) ₹144
  3. 3.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 27 days (c) 26 days (d) 10 days
  4. 4.If 5 notebooks cost ₹55, how much do 8 notebooks cost? (a) ₹440 (b) ₹58 (c) ₹99 (d) ₹88
  5. 5.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 16 days (c) 24 days (d) 8 days
  6. 6.If 6 kites cost ₹138, how much do 5 kites cost? (a) ₹690 (b) ₹138 (c) ₹137 (d) ₹115
  7. 7.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹14 (b) ₹7 (c) ₹42 (d) ₹35
  8. 8.If 9 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹32 (b) ₹36 (c) ₹288 (d) ₹35
  9. 9.₹189 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹163 (b) ₹189 (c) ₹27 (d) ₹162
  10. 10.If 9 notebooks cost ₹162, how much do 4 notebooks cost? (a) ₹157 (b) ₹648 (c) ₹72 (d) ₹90
  11. 11.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹216 (b) ₹72 (c) ₹90 (d) ₹55
  12. 12.If 8 pens cost ₹72, how much do 9 pens cost? (a) ₹90 (b) ₹81 (c) ₹73 (d) ₹648
  13. 13.If 7 pens cost ₹105, how much do 10 pens cost? (a) ₹1050 (b) ₹150 (c) ₹165 (d) ₹108
  14. 14.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 39 days (c) 40 days (d) 9 days
  15. 15.If 4 notebooks cost ₹60, how much do 8 notebooks cost? (a) ₹480 (b) ₹135 (c) ₹64 (d) ₹120
  16. 16.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹230 (b) ₹184 (c) ₹46 (d) ₹138
  17. 17.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 11 days (d) 3 days
  18. 18.If 8 kites cost ₹80, how much do 4 kites cost? (a) ₹320 (b) ₹76 (c) ₹50 (d) ₹40
  19. 19.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 14 days (c) 10 days (d) 15 days
  20. 20.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 6 days (d) 12 days
  21. 21.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 23 days (d) 25 days
  22. 22.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 19 days (d) 11 days
  23. 23.If 9 pens cost ₹180, how much do 7 pens cost? (a) ₹160 (b) ₹1260 (c) ₹140 (d) ₹178
  24. 24.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹11 (b) ₹110 (c) ₹99 (d) ₹44
  25. 25.If 8 notebooks cost ₹56, how much do 6 notebooks cost? (a) ₹42 (b) ₹336 (c) ₹49 (d) ₹54
  26. 26.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 16 days (d) 11 days
  27. 27.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹162 (d) ₹135
  28. 28.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹16 (b) ₹36 (c) ₹8 (d) ₹56
  29. 29.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 22 days (d) 21 days
  30. 30.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 5 days (d) 6 days
  31. 31.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
  32. 32.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 40 days (d) 39 days
  33. 33.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹54 (b) ₹119 (c) ₹102 (d) ₹306
  34. 34.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹27 (c) ₹81 (d) ₹9
  35. 35.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 16 days (c) 13 days (d) 17 days
  36. 36.If 6 kites cost ₹102, how much do 12 kites cost? (a) ₹204 (b) ₹1224 (c) ₹108 (d) ₹221
  37. 37.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹189 (b) ₹135 (c) ₹27 (d) ₹81
  38. 38.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹203 (b) ₹145 (c) ₹29 (d) ₹174
  39. 39.If 4 mangoes cost ₹88, how much do 7 mangoes cost? (a) ₹176 (b) ₹91 (c) ₹616 (d) ₹154
  40. 40.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 19 days (d) 2 days

Answer key

  1. 6 days
  2. ₹132
  3. 26 days
  4. ₹88
  5. 24 days
  6. ₹115
  7. ₹35
  8. ₹32
  9. ₹162
  10. ₹72
  11. ₹72
  12. ₹81
  13. ₹150
  14. 39 days
  15. ₹120
  16. ₹230
  17. 21 days
  18. ₹40
  19. 14 days
  20. 18 days
  21. 24 days
  22. 45 days
  23. ₹140
  24. ₹99
  25. ₹42
  26. 15 days
  27. ₹135
  28. ₹56
  29. 21 days
  30. 5 days
  31. 7 days
  32. 39 days
  33. ₹102
  34. ₹72
  35. 16 days
  36. ₹204
  37. ₹189
  38. ₹174
  39. ₹154
  40. 3 days

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