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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 498 · 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. 1.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 7 days (d) 2 days
  2. 2.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹170 (b) ₹238 (c) ₹34 (d) ₹102
  3. 3.If 5 kites cost ₹15, how much do 3 kites cost? (a) ₹12 (b) ₹13 (c) ₹9 (d) ₹45
  4. 4.₹104 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹52 (d) ₹78
  5. 5.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹48 (b) ₹36 (c) ₹72 (d) ₹25
  6. 6.If 5 kites cost ₹80, how much do 8 kites cost? (a) ₹83 (b) ₹640 (c) ₹144 (d) ₹128
  7. 7.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹96 (b) ₹88 (c) ₹16 (d) ₹80
  8. 8.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹78 (b) ₹117 (c) ₹39 (d) ₹156
  9. 9.₹341 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹155 (b) ₹186 (c) ₹31 (d) ₹217
  10. 10.If 3 notebooks cost ₹33, how much do 6 notebooks cost? (a) ₹198 (b) ₹77 (c) ₹66 (d) ₹36
  11. 11.If 7 notebooks cost ₹175, how much do 11 notebooks cost? (a) ₹300 (b) ₹275 (c) ₹179 (d) ₹1925
  12. 12.If 8 pens cost ₹176, how much do 5 pens cost? (a) ₹880 (b) ₹110 (c) ₹173 (d) ₹132
  13. 13.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹225 (d) ₹450
  14. 14.If 4 pens cost ₹84, how much do 6 pens cost? (a) ₹147 (b) ₹504 (c) ₹86 (d) ₹126
  15. 15.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 19 days (d) 35 days
  16. 16.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹240 (b) ₹216 (c) ₹24 (d) ₹120
  17. 17.If 4 kites cost ₹56, how much do 8 kites cost? (a) ₹112 (b) ₹448 (c) ₹126 (d) ₹60
  18. 18.5 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
  19. 19.If 9 kites cost ₹72, how much do 5 kites cost? (a) ₹48 (b) ₹68 (c) ₹40 (d) ₹360
  20. 20.₹100 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹75 (b) ₹50 (c) ₹100 (d) ₹25
  21. 21.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 22 days (d) 23 days
  22. 22.₹150 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹75 (c) ₹30 (d) ₹90
  23. 23.If 8 notebooks cost ₹200, how much do 9 notebooks cost? (a) ₹201 (b) ₹225 (c) ₹250 (d) ₹1800
  24. 24.If 6 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹36 (b) ₹198 (c) ₹23 (d) ₹33
  25. 25.If 5 kites cost ₹100, how much do 12 kites cost? (a) ₹1200 (b) ₹107 (c) ₹240 (d) ₹260
  26. 26.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹205 (b) ₹369 (c) ₹41 (d) ₹410
  27. 27.If 8 pens cost ₹160, how much do 10 pens cost? (a) ₹1600 (b) ₹162 (c) ₹220 (d) ₹200
  28. 28.If 6 kites cost ₹138, how much do 12 kites cost? (a) ₹276 (b) ₹1656 (c) ₹144 (d) ₹299
  29. 29.If 5 notebooks cost ₹115, how much do 6 notebooks cost? (a) ₹690 (b) ₹116 (c) ₹138 (d) ₹161
  30. 30.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹78 (d) ₹26
  31. 31.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹10 (d) ₹25
  32. 32.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹156 (b) ₹117 (c) ₹78 (d) ₹39
  33. 33.If 3 pens cost ₹33, how much do 4 pens cost? (a) ₹55 (b) ₹132 (c) ₹44 (d) ₹34
  34. 34.If 4 mangoes cost ₹20, how much do 12 mangoes cost? (a) ₹60 (b) ₹240 (c) ₹28 (d) ₹65
  35. 35.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹25 (c) ₹5 (d) ₹35
  36. 36.If 5 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹42 (b) ₹28 (c) ₹67 (d) ₹140
  37. 37.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹18 (b) ₹13 (c) ₹60 (d) ₹15
  38. 38.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 2 days
  39. 39.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
  40. 40.₹125 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹100 (b) ₹101 (c) ₹125 (d) ₹25

Answer key

  1. 8 days
  2. ₹238
  3. ₹9
  4. ₹78
  5. ₹36
  6. ₹128
  7. ₹96
  8. ₹117
  9. ₹186
  10. ₹66
  11. ₹275
  12. ₹110
  13. ₹405
  14. ₹126
  15. 35 days
  16. ₹216
  17. ₹112
  18. 25 days
  19. ₹40
  20. ₹75
  21. 22 days
  22. ₹90
  23. ₹225
  24. ₹33
  25. ₹240
  26. ₹369
  27. ₹200
  28. ₹276
  29. ₹138
  30. ₹65
  31. ₹30
  32. ₹117
  33. ₹44
  34. ₹60
  35. ₹45
  36. ₹28
  37. ₹15
  38. 3 days
  39. 45 days
  40. ₹100

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