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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 202 · 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 6 mangoes cost ₹108, how much do 9 mangoes cost? (a) ₹972 (b) ₹180 (c) ₹162 (d) ₹111
  2. 2.If 7 notebooks cost ₹133, how much do 3 notebooks cost? (a) ₹76 (b) ₹399 (c) ₹129 (d) ₹57
  3. 3.₹135 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹108 (b) ₹135 (c) ₹109 (d) ₹27
  4. 4.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 29 days (c) 28 days (d) 13 days
  5. 5.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 29 days (c) 16 days (d) 8 days
  6. 6.If 2 notebooks cost ₹6, how much do 12 notebooks cost? (a) ₹16 (b) ₹72 (c) ₹36 (d) ₹39
  7. 7.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹40 (b) ₹10 (c) ₹90 (d) ₹65
  8. 8.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 23 days (d) 24 days
  9. 9.If 8 notebooks cost ₹72, how much do 4 notebooks cost? (a) ₹68 (b) ₹45 (c) ₹288 (d) ₹36
  10. 10.If 2 mangoes cost ₹24, how much do 3 mangoes cost? (a) ₹72 (b) ₹48 (c) ₹25 (d) ₹36
  11. 11.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 36 days (d) 35 days
  12. 12.If 9 kites cost ₹36, how much do 12 kites cost? (a) ₹432 (b) ₹39 (c) ₹52 (d) ₹48
  13. 13.8 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 10 days (d) 8 days
  14. 14.If 2 kites cost ₹6, how much do 3 kites cost? (a) ₹18 (b) ₹7 (c) ₹12 (d) ₹9
  15. 15.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 9 days (d) 21 days
  16. 16.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 6 days (d) 5 days
  17. 17.If 2 kites cost ₹18, how much do 10 kites cost? (a) ₹26 (b) ₹90 (c) ₹99 (d) ₹180
  18. 18.If 3 mangoes cost ₹57, how much do 8 mangoes cost? (a) ₹62 (b) ₹171 (c) ₹456 (d) ₹152
  19. 19.If 7 kites cost ₹126, how much do 8 kites cost? (a) ₹127 (b) ₹1008 (c) ₹144 (d) ₹162
  20. 20.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 7 days
  21. 21.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 7 days (c) 13 days (d) 5 days
  22. 22.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹156 (b) ₹216 (c) ₹96 (d) ₹24
  23. 23.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹192 (b) ₹312 (c) ₹48 (d) ₹432
  24. 24.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹28 (b) ₹140 (c) ₹98 (d) ₹56
  25. 25.If 6 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹432 (b) ₹90 (c) ₹72 (d) ₹106
  26. 26.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹30 (b) ₹50 (c) ₹10 (d) ₹70
  27. 27.If 4 pens cost ₹64, how much do 2 pens cost? (a) ₹48 (b) ₹32 (c) ₹128 (d) ₹62
  28. 28.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹336 (d) ₹240
  29. 29.If 8 mangoes cost ₹144, how much do 4 mangoes cost? (a) ₹140 (b) ₹90 (c) ₹72 (d) ₹576
  30. 30.7 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
  31. 31.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹258 (d) ₹129
  32. 32.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 15 days (d) 3 days
  33. 33.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 48 days (b) 21 days (c) 3 days (d) 4 days
  34. 34.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 19 days (d) 7 days
  35. 35.If 2 notebooks cost ₹22, how much do 6 notebooks cost? (a) ₹77 (b) ₹26 (c) ₹66 (d) ₹132
  36. 36.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 3 days
  37. 37.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 6 days (d) 10 days
  38. 38.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 1 day (d) 11 days
  39. 39.If 9 kites cost ₹27, how much do 12 kites cost? (a) ₹39 (b) ₹30 (c) ₹324 (d) ₹36
  40. 40.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹324 (b) ₹36 (c) ₹162 (d) ₹288

Answer key

  1. ₹162
  2. ₹57
  3. ₹108
  4. 28 days
  5. 28 days
  6. ₹36
  7. ₹90
  8. 24 days
  9. ₹36
  10. ₹36
  11. 35 days
  12. ₹48
  13. 8 days
  14. ₹9
  15. 5 days
  16. 5 days
  17. ₹90
  18. ₹152
  19. ₹144
  20. 3 days
  21. 20 days
  22. ₹216
  23. ₹432
  24. ₹140
  25. ₹72
  26. ₹70
  27. ₹32
  28. ₹336
  29. ₹72
  30. 7 days
  31. ₹215
  32. 27 days
  33. 3 days
  34. 39 days
  35. ₹66
  36. 2 days
  37. 16 days
  38. 10 days
  39. ₹36
  40. ₹288

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