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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 592 · 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.₹650 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹325 (b) ₹450 (c) ₹50 (d) ₹200
  2. 2.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹261 (b) ₹290 (c) ₹29 (d) ₹145
  3. 3.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 12 days
  4. 4.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 9 days (d) 11 days
  5. 5.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 9 days (d) 11 days
  6. 6.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 16 days (d) 12 days
  7. 7.If 2 pens cost ₹18, how much do 12 pens cost? (a) ₹216 (b) ₹28 (c) ₹108 (d) ₹117
  8. 8.If 6 pens cost ₹30, how much do 12 pens cost? (a) ₹360 (b) ₹36 (c) ₹60 (d) ₹65
  9. 9.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 23 days (d) 14 days
  10. 10.₹352 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹128 (b) ₹224 (c) ₹176 (d) ₹32
  11. 11.If 5 kites cost ₹20, how much do 9 kites cost? (a) ₹40 (b) ₹24 (c) ₹180 (d) ₹36
  12. 12.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹450 (d) ₹350
  13. 13.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹43 (b) ₹258 (c) ₹172 (d) ₹215
  14. 14.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹51 (b) ₹34 (c) ₹17 (d) ₹35
  15. 15.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹75 (c) ₹15 (d) ₹105
  16. 16.₹602 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹43 (b) ₹387 (c) ₹215 (d) ₹301
  17. 17.₹198 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹99 (b) ₹126 (c) ₹72 (d) ₹18
  18. 18.If 8 notebooks cost ₹40, how much do 9 notebooks cost? (a) ₹45 (b) ₹360 (c) ₹41 (d) ₹50
  19. 19.If 6 mangoes cost ₹150, how much do 4 mangoes cost? (a) ₹125 (b) ₹600 (c) ₹100 (d) ₹148
  20. 20.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹44 (b) ₹308 (c) ₹176 (d) ₹352
  21. 21.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹6 (b) ₹18 (c) ₹30 (d) ₹24
  22. 22.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 8 days (c) 20 days (d) 42 days
  23. 23.If 2 notebooks cost ₹24, how much do 6 notebooks cost? (a) ₹84 (b) ₹144 (c) ₹72 (d) ₹28
  24. 24.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 36 days (b) 20 days (c) 4 days (d) 5 days
  25. 25.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 8 days (d) 5 days
  26. 26.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹184 (b) ₹23 (c) ₹92 (d) ₹161
  27. 27.If 8 notebooks cost ₹32, how much do 2 notebooks cost? (a) ₹26 (b) ₹64 (c) ₹12 (d) ₹8
  28. 28.If 2 kites cost ₹8, how much do 9 kites cost? (a) ₹15 (b) ₹36 (c) ₹40 (d) ₹72
  29. 29.If 4 mangoes cost ₹88, how much do 3 mangoes cost? (a) ₹88 (b) ₹66 (c) ₹87 (d) ₹264
  30. 30.If 9 pens cost ₹81, how much do 8 pens cost? (a) ₹648 (b) ₹80 (c) ₹81 (d) ₹72
  31. 31.₹15 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹10 (c) ₹5 (d) ₹11
  32. 32.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 10 days (c) 14 days (d) 6 days
  33. 33.If 8 kites cost ₹168, how much do 9 kites cost? (a) ₹1512 (b) ₹210 (c) ₹169 (d) ₹189
  34. 34.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹96 (d) ₹72
  35. 35.If 7 notebooks cost ₹119, how much do 3 notebooks cost? (a) ₹115 (b) ₹51 (c) ₹357 (d) ₹68
  36. 36.₹276 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹230 (b) ₹276 (c) ₹46 (d) ₹138
  37. 37.If 7 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹45 (b) ₹36 (c) ₹252 (d) ₹60
  38. 38.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹184 (b) ₹69 (c) ₹207 (d) ₹23
  39. 39.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 4 days (d) 3 days
  40. 40.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹55 (b) ₹26 (c) ₹200 (d) ₹50

Answer key

  1. ₹450
  2. ₹261
  3. 12 days
  4. 12 days
  5. 16 days
  6. 12 days
  7. ₹108
  8. ₹60
  9. 22 days
  10. ₹224
  11. ₹36
  12. ₹450
  13. ₹215
  14. ₹34
  15. ₹105
  16. ₹387
  17. ₹126
  18. ₹45
  19. ₹100
  20. ₹308
  21. ₹30
  22. 42 days
  23. ₹72
  24. 4 days
  25. 4 days
  26. ₹161
  27. ₹8
  28. ₹36
  29. ₹66
  30. ₹72
  31. ₹10
  32. 24 days
  33. ₹189
  34. ₹72
  35. ₹51
  36. ₹230
  37. ₹36
  38. ₹184
  39. 3 days
  40. ₹50

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