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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 487 · 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. 1.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 8 days (d) 9 days
  2. 2.If 3 pens cost ₹54, how much do 4 pens cost? (a) ₹216 (b) ₹90 (c) ₹55 (d) ₹72
  3. 3.If 9 mangoes cost ₹153, how much do 2 mangoes cost? (a) ₹51 (b) ₹34 (c) ₹306 (d) ₹146
  4. 4.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 48 days (b) 3 days (c) 6 days (d) 18 days
  5. 5.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹29 (b) ₹116 (c) ₹174 (d) ₹145
  6. 6.If 8 mangoes cost ₹48, how much do 10 mangoes cost? (a) ₹66 (b) ₹60 (c) ₹480 (d) ₹50
  7. 7.If 3 mangoes cost ₹39, how much do 6 mangoes cost? (a) ₹42 (b) ₹234 (c) ₹91 (d) ₹78
  8. 8.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹43 (b) ₹86 (c) ₹430 (d) ₹387
  9. 9.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 31 days (c) 16 days (d) 30 days
  10. 10.If 9 mangoes cost ₹198, how much do 4 mangoes cost? (a) ₹193 (b) ₹110 (c) ₹88 (d) ₹792
  11. 11.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 27 days (d) 15 days
  12. 12.If 4 mangoes cost ₹96, how much do 8 mangoes cost? (a) ₹216 (b) ₹768 (c) ₹192 (d) ₹100
  13. 13.If 5 mangoes cost ₹80, how much do 8 mangoes cost? (a) ₹144 (b) ₹83 (c) ₹640 (d) ₹128
  14. 14.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 17 days (d) 9 days
  15. 15.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹35 (c) ₹5 (d) ₹30
  16. 16.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹35 (b) ₹14 (c) ₹42 (d) ₹7
  17. 17.If 8 notebooks cost ₹176, how much do 7 notebooks cost? (a) ₹154 (b) ₹1232 (c) ₹176 (d) ₹175
  18. 18.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹31 (d) ₹30
  19. 19.₹108 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹9 (b) ₹54 (c) ₹63 (d) ₹45
  20. 20.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 7 days (d) 6 days
  21. 21.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹301 (d) ₹258
  22. 22.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹80 (d) ₹40
  23. 23.₹423 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹376 (d) ₹94
  24. 24.If 7 mangoes cost ₹84, how much do 9 mangoes cost? (a) ₹86 (b) ₹120 (c) ₹756 (d) ₹108
  25. 25.If 3 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹100 (b) ₹300 (c) ₹37 (d) ₹110
  26. 26.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 21 days
  27. 27.If 2 kites cost ₹6, how much do 5 kites cost? (a) ₹15 (b) ₹9 (c) ₹18 (d) ₹30
  28. 28.If 6 kites cost ₹30, how much do 10 kites cost? (a) ₹300 (b) ₹34 (c) ₹55 (d) ₹50
  29. 29.If 9 notebooks cost ₹225, how much do 6 notebooks cost? (a) ₹1350 (b) ₹222 (c) ₹175 (d) ₹150
  30. 30.If 6 mangoes cost ₹108, how much do 7 mangoes cost? (a) ₹756 (b) ₹126 (c) ₹144 (d) ₹109
  31. 31.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 32 days (d) 17 days
  32. 32.If 6 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹32 (b) ₹40 (c) ₹45 (d) ₹240
  33. 33.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹75 (d) ₹100
  34. 34.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
  35. 35.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹243 (d) ₹216
  36. 36.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 11 days
  37. 37.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 7 days (c) 19 days (d) 52 days
  38. 38.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹27 (b) ₹54 (c) ₹216 (d) ₹189
  39. 39.If 9 mangoes cost ₹225, how much do 6 mangoes cost? (a) ₹222 (b) ₹175 (c) ₹150 (d) ₹1350
  40. 40.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹40 (d) ₹16

Answer key

  1. 8 days
  2. ₹72
  3. ₹34
  4. 48 days
  5. ₹145
  6. ₹60
  7. ₹78
  8. ₹387
  9. 30 days
  10. ₹88
  11. 27 days
  12. ₹192
  13. ₹128
  14. 26 days
  15. ₹35
  16. ₹35
  17. ₹154
  18. ₹30
  19. ₹63
  20. 7 days
  21. ₹258
  22. ₹70
  23. ₹329
  24. ₹108
  25. ₹100
  26. 6 days
  27. ₹15
  28. ₹50
  29. ₹150
  30. ₹126
  31. 32 days
  32. ₹40
  33. ₹125
  34. 3 days
  35. ₹216
  36. 10 days
  37. 52 days
  38. ₹189
  39. ₹150
  40. ₹64

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