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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 30 · 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. 1.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 7 days (d) 10 days
  2. 2.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹294 (b) ₹245 (c) ₹49 (d) ₹343
  3. 3.If 8 notebooks cost ₹112, how much do 12 notebooks cost? (a) ₹116 (b) ₹168 (c) ₹1344 (d) ₹182
  4. 4.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 20 days (d) 5 days
  5. 5.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹53 (b) ₹65 (c) ₹13 (d) ₹52
  6. 6.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 9 days
  7. 7.If 4 pens cost ₹52, how much do 5 pens cost? (a) ₹260 (b) ₹53 (c) ₹65 (d) ₹78
  8. 8.If 7 mangoes cost ₹168, how much do 11 mangoes cost? (a) ₹1848 (b) ₹264 (c) ₹288 (d) ₹172
  9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 8 days (d) 56 days
  10. 10.If 3 pens cost ₹21, how much do 4 pens cost? (a) ₹22 (b) ₹84 (c) ₹35 (d) ₹28
  11. 11.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹104 (d) ₹78
  12. 12.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 19 days (d) 7 days
  13. 13.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹162 (b) ₹36 (c) ₹288 (d) ₹324
  14. 14.If 4 kites cost ₹20, how much do 5 kites cost? (a) ₹30 (b) ₹21 (c) ₹25 (d) ₹100
  15. 15.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 19 days (d) 12 days
  16. 16.₹385 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹245 (b) ₹35 (c) ₹140 (d) ₹280
  17. 17.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹50 (d) ₹45
  18. 18.If 9 mangoes cost ₹180, how much do 4 mangoes cost? (a) ₹80 (b) ₹720 (c) ₹175 (d) ₹100
  19. 19.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 20 days (d) 28 days
  20. 20.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹41 (b) ₹205 (c) ₹246 (d) ₹287
  21. 21.If 6 kites cost ₹24, how much do 2 kites cost? (a) ₹12 (b) ₹8 (c) ₹20 (d) ₹48
  22. 22.If 6 pens cost ₹102, how much do 7 pens cost? (a) ₹136 (b) ₹714 (c) ₹103 (d) ₹119
  23. 23.If 2 mangoes cost ₹20, how much do 11 mangoes cost? (a) ₹120 (b) ₹29 (c) ₹220 (d) ₹110
  24. 24.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹252 (d) ₹231
  25. 25.If 6 pens cost ₹96, how much do 10 pens cost? (a) ₹176 (b) ₹960 (c) ₹160 (d) ₹100
  26. 26.If 8 kites cost ₹192, how much do 9 kites cost? (a) ₹1728 (b) ₹240 (c) ₹193 (d) ₹216
  27. 27.If 7 kites cost ₹161, how much do 5 kites cost? (a) ₹115 (b) ₹805 (c) ₹138 (d) ₹159
  28. 28.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹65 (b) ₹52 (c) ₹39 (d) ₹13
  29. 29.₹450 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹225 (b) ₹100 (c) ₹50 (d) ₹350
  30. 30.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹9 (d) ₹27
  31. 31.If 3 pens cost ₹24, how much do 9 pens cost? (a) ₹80 (b) ₹72 (c) ₹30 (d) ₹216
  32. 32.If 4 mangoes cost ₹72, how much do 12 mangoes cost? (a) ₹864 (b) ₹216 (c) ₹234 (d) ₹80
  33. 33.If 6 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹53 (b) ₹270 (c) ₹54 (d) ₹45
  34. 34.If 3 pens cost ₹54, how much do 4 pens cost? (a) ₹90 (b) ₹72 (c) ₹216 (d) ₹55
  35. 35.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  36. 36.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 6 days (d) 4 days
  37. 37.If 3 pens cost ₹39, how much do 2 pens cost? (a) ₹26 (b) ₹39 (c) ₹38 (d) ₹78
  38. 38.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 17 days
  39. 39.If 8 pens cost ₹88, how much do 4 pens cost? (a) ₹55 (b) ₹44 (c) ₹84 (d) ₹352
  40. 40.If 4 kites cost ₹92, how much do 11 kites cost? (a) ₹1012 (b) ₹276 (c) ₹253 (d) ₹99

Answer key

  1. 10 days
  2. ₹343
  3. ₹168
  4. 20 days
  5. ₹52
  6. 4 days
  7. ₹65
  8. ₹264
  9. 56 days
  10. ₹28
  11. ₹78
  12. 39 days
  13. ₹288
  14. ₹25
  15. 18 days
  16. ₹245
  17. ₹45
  18. ₹80
  19. 7 days
  20. ₹287
  21. ₹8
  22. ₹119
  23. ₹110
  24. ₹252
  25. ₹160
  26. ₹216
  27. ₹115
  28. ₹52
  29. ₹350
  30. ₹27
  31. ₹72
  32. ₹216
  33. ₹45
  34. ₹72
  35. 25 days
  36. 5 days
  37. ₹26
  38. 21 days
  39. ₹44
  40. ₹253

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