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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 619 · 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.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹27 (b) ₹9 (c) ₹72 (d) ₹81
  2. 2.If 2 pens cost ₹42, how much do 12 pens cost? (a) ₹504 (b) ₹252 (c) ₹52 (d) ₹273
  3. 3.If 4 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹420 (b) ₹120 (c) ₹63 (d) ₹105
  4. 4.If 2 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹23 (b) ₹126 (c) ₹63 (d) ₹72
  5. 5.₹210 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹120 (b) ₹105 (c) ₹90 (d) ₹30
  6. 6.If 7 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹504 (b) ₹78 (c) ₹72 (d) ₹47
  7. 7.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 1 day (d) 11 days
  8. 8.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 8 days (d) 6 days
  9. 9.If 3 mangoes cost ₹36, how much do 11 mangoes cost? (a) ₹44 (b) ₹132 (c) ₹396 (d) ₹144
  10. 10.If 3 notebooks cost ₹60, how much do 2 notebooks cost? (a) ₹59 (b) ₹60 (c) ₹120 (d) ₹40
  11. 11.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 8 days (d) 9 days
  12. 12.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 13 days (d) 7 days
  13. 13.₹222 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹37 (b) ₹185 (c) ₹111 (d) ₹222
  14. 14.If 6 pens cost ₹120, how much do 4 pens cost? (a) ₹480 (b) ₹100 (c) ₹80 (d) ₹118
  15. 15.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 4 days (d) 8 days
  16. 16.If 5 notebooks cost ₹85, how much do 9 notebooks cost? (a) ₹170 (b) ₹765 (c) ₹89 (d) ₹153
  17. 17.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹145 (d) ₹116
  18. 18.If 7 kites cost ₹98, how much do 10 kites cost? (a) ₹140 (b) ₹980 (c) ₹101 (d) ₹154
  19. 19.If 9 pens cost ₹36, how much do 3 pens cost? (a) ₹12 (b) ₹16 (c) ₹108 (d) ₹30
  20. 20.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 25 days (c) 12 days (d) 4 days
  21. 21.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 8 days (d) 2 days
  22. 22.If 6 kites cost ₹42, how much do 9 kites cost? (a) ₹45 (b) ₹378 (c) ₹70 (d) ₹63
  23. 23.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹245 (d) ₹196
  24. 24.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹60 (b) ₹42 (c) ₹12 (d) ₹24
  25. 25.If 7 pens cost ₹84, how much do 6 pens cost? (a) ₹504 (b) ₹84 (c) ₹83 (d) ₹72
  26. 26.If 7 notebooks cost ₹161, how much do 12 notebooks cost? (a) ₹299 (b) ₹166 (c) ₹1932 (d) ₹276
  27. 27.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹36 (b) ₹288 (c) ₹234 (d) ₹180
  28. 28.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 7 days (d) 28 days
  29. 29.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹39 (c) ₹13 (d) ₹27
  30. 30.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 32 days (d) 14 days
  31. 31.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
  32. 32.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹15 (b) ₹121 (c) ₹135 (d) ₹120
  33. 33.If 6 notebooks cost ₹132, how much do 12 notebooks cost? (a) ₹286 (b) ₹1584 (c) ₹264 (d) ₹138
  34. 34.If 8 mangoes cost ₹144, how much do 10 mangoes cost? (a) ₹146 (b) ₹1440 (c) ₹198 (d) ₹180
  35. 35.If 5 mangoes cost ₹25, how much do 6 mangoes cost? (a) ₹30 (b) ₹35 (c) ₹26 (d) ₹150
  36. 36.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  37. 37.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 11 days (d) 7 days
  38. 38.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
  39. 39.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 4 days
  40. 40.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 29 days (d) 13 days

Answer key

  1. ₹72
  2. ₹252
  3. ₹105
  4. ₹63
  5. ₹120
  6. ₹72
  7. 21 days
  8. 7 days
  9. ₹132
  10. ₹40
  11. 2 days
  12. 6 days
  13. ₹185
  14. ₹80
  15. 9 days
  16. ₹153
  17. ₹116
  18. ₹140
  19. ₹12
  20. 24 days
  21. 2 days
  22. ₹63
  23. ₹245
  24. ₹60
  25. ₹72
  26. ₹276
  27. ₹288
  28. 28 days
  29. ₹26
  30. 32 days
  31. 5 days
  32. ₹120
  33. ₹264
  34. ₹180
  35. ₹30
  36. 9 days
  37. 10 days
  38. 7 days
  39. 6 days
  40. 28 days

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