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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 244 · 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. 1.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
  2. 2.If 5 pens cost ₹55, how much do 8 pens cost? (a) ₹440 (b) ₹99 (c) ₹58 (d) ₹88
  3. 3.If 7 pens cost ₹140, how much do 3 pens cost? (a) ₹60 (b) ₹420 (c) ₹80 (d) ₹136
  4. 4.If 3 notebooks cost ₹66, how much do 10 notebooks cost? (a) ₹73 (b) ₹660 (c) ₹242 (d) ₹220
  5. 5.If 7 kites cost ₹70, how much do 10 kites cost? (a) ₹110 (b) ₹73 (c) ₹700 (d) ₹100
  6. 6.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 39 days (d) 40 days
  7. 7.₹360 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹210 (b) ₹30 (c) ₹150 (d) ₹180
  8. 8.If 9 notebooks cost ₹180, how much do 5 notebooks cost? (a) ₹100 (b) ₹176 (c) ₹900 (d) ₹120
  9. 9.If 6 notebooks cost ₹114, how much do 7 notebooks cost? (a) ₹133 (b) ₹115 (c) ₹152 (d) ₹798
  10. 10.If 5 notebooks cost ₹75, how much do 6 notebooks cost? (a) ₹76 (b) ₹450 (c) ₹90 (d) ₹105
  11. 11.If 3 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹72 (b) ₹26 (c) ₹198 (d) ₹66
  12. 12.₹93 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹31 (b) ₹93 (c) ₹63 (d) ₹62
  13. 13.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 1 day
  14. 14.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹171 (b) ₹152 (c) ₹38 (d) ₹190
  15. 15.If 2 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹19 (b) ₹60 (c) ₹108 (d) ₹54
  16. 16.₹120 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹120 (b) ₹60 (c) ₹80 (d) ₹40
  17. 17.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 22 days (d) 21 days
  18. 18.If 9 mangoes cost ₹225, how much do 4 mangoes cost? (a) ₹100 (b) ₹125 (c) ₹220 (d) ₹900
  19. 19.If 9 kites cost ₹171, how much do 6 kites cost? (a) ₹168 (b) ₹1026 (c) ₹114 (d) ₹133
  20. 20.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹225 (c) ₹135 (d) ₹180
  21. 21.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹210 (b) ₹168 (c) ₹42 (d) ₹189
  22. 22.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹63 (b) ₹9 (c) ₹45 (d) ₹27
  23. 23.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹110 (d) ₹120
  24. 24.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 3 days (d) 4 days
  25. 25.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹376 (c) ₹47 (d) ₹235
  26. 26.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 5 days (d) 6 days
  27. 27.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹60 (b) ₹54 (c) ₹48 (d) ₹12
  28. 28.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹34 (b) ₹102 (c) ₹238 (d) ₹170
  29. 29.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹21 (b) ₹7 (c) ₹63 (d) ₹56
  30. 30.If 2 notebooks cost ₹42, how much do 9 notebooks cost? (a) ₹189 (b) ₹49 (c) ₹210 (d) ₹378
  31. 31.If 9 mangoes cost ₹207, how much do 10 mangoes cost? (a) ₹208 (b) ₹230 (c) ₹2070 (d) ₹253
  32. 32.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 12 days (d) 16 days
  33. 33.If 5 notebooks cost ₹125, how much do 3 notebooks cost? (a) ₹123 (b) ₹100 (c) ₹375 (d) ₹75
  34. 34.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹27 (b) ₹243 (c) ₹135 (d) ₹270
  35. 35.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹410 (b) ₹41 (c) ₹164 (d) ₹369
  36. 36.If 2 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹15 (b) ₹30 (c) ₹36 (d) ₹60
  37. 37.If 7 pens cost ₹126, how much do 6 pens cost? (a) ₹756 (b) ₹126 (c) ₹108 (d) ₹125
  38. 38.₹308 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹140 (b) ₹154 (c) ₹28 (d) ₹168
  39. 39.If 4 kites cost ₹24, how much do 7 kites cost? (a) ₹27 (b) ₹168 (c) ₹42 (d) ₹48
  40. 40.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹81 (d) ₹45

Answer key

  1. 3 days
  2. ₹88
  3. ₹60
  4. ₹220
  5. ₹100
  6. 39 days
  7. ₹210
  8. ₹100
  9. ₹133
  10. ₹90
  11. ₹66
  12. ₹62
  13. 7 days
  14. ₹190
  15. ₹54
  16. ₹80
  17. 21 days
  18. ₹100
  19. ₹114
  20. ₹225
  21. ₹210
  22. ₹63
  23. ₹120
  24. 3 days
  25. ₹376
  26. 5 days
  27. ₹60
  28. ₹238
  29. ₹56
  30. ₹189
  31. ₹230
  32. 16 days
  33. ₹75
  34. ₹243
  35. ₹369
  36. ₹30
  37. ₹108
  38. ₹168
  39. ₹42
  40. ₹72

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