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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 271 · 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.If 8 mangoes cost ₹32, how much do 10 mangoes cost? (a) ₹40 (b) ₹320 (c) ₹34 (d) ₹44
  2. 2.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹300 (d) ₹150
  3. 3.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹36 (d) ₹48
  4. 4.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 26 days (d) 27 days
  5. 5.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹40 (d) ₹48
  6. 6.7 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) 15 days (d) 7 days
  7. 7.If 7 pens cost ₹133, how much do 12 pens cost? (a) ₹138 (b) ₹228 (c) ₹247 (d) ₹1596
  8. 8.If 8 pens cost ₹160, how much do 4 pens cost? (a) ₹156 (b) ₹640 (c) ₹100 (d) ₹80
  9. 9.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 11 days (d) 7 days
  10. 10.If 9 pens cost ₹225, how much do 6 pens cost? (a) ₹175 (b) ₹222 (c) ₹1350 (d) ₹150
  11. 11.If 8 pens cost ₹120, how much do 3 pens cost? (a) ₹115 (b) ₹60 (c) ₹360 (d) ₹45
  12. 12.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹217 (b) ₹155 (c) ₹31 (d) ₹186
  13. 13.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹42 (b) ₹30 (c) ₹18 (d) ₹6
  14. 14.If 9 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹30 (b) ₹108 (c) ₹16 (d) ₹12
  15. 15.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹30 (c) ₹25 (d) ₹27
  16. 16.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹70 (d) ₹50
  17. 17.If 6 kites cost ₹96, how much do 5 kites cost? (a) ₹80 (b) ₹480 (c) ₹96 (d) ₹95
  18. 18.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 6 days (d) 2 days
  19. 19.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹78 (b) ₹60 (c) ₹96 (d) ₹12
  20. 20.If 6 notebooks cost ₹42, how much do 3 notebooks cost? (a) ₹39 (b) ₹28 (c) ₹21 (d) ₹126
  21. 21.If 8 mangoes cost ₹144, how much do 12 mangoes cost? (a) ₹216 (b) ₹148 (c) ₹1728 (d) ₹234
  22. 22.If 2 mangoes cost ₹16, how much do 7 mangoes cost? (a) ₹64 (b) ₹112 (c) ₹21 (d) ₹56
  23. 23.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹21 (b) ₹14 (c) ₹7 (d) ₹28
  24. 24.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 8 days (d) 7 days
  25. 25.If 2 pens cost ₹38, how much do 4 pens cost? (a) ₹152 (b) ₹95 (c) ₹40 (d) ₹76
  26. 26.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹5 (b) ₹45 (c) ₹10 (d) ₹50
  27. 27.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 19 days
  28. 28.5 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) 4 days (d) 5 days
  29. 29.If 6 pens cost ₹60, how much do 2 pens cost? (a) ₹30 (b) ₹120 (c) ₹56 (d) ₹20
  30. 30.If 9 kites cost ₹81, how much do 4 kites cost? (a) ₹45 (b) ₹36 (c) ₹324 (d) ₹76
  31. 31.If 2 pens cost ₹14, how much do 9 pens cost? (a) ₹126 (b) ₹70 (c) ₹63 (d) ₹21
  32. 32.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 9 days (d) 4 days
  33. 33.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 7 days
  34. 34.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
  35. 35.₹220 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹220 (b) ₹198 (c) ₹110 (d) ₹22
  36. 36.If 2 mangoes cost ₹26, how much do 7 mangoes cost? (a) ₹104 (b) ₹31 (c) ₹182 (d) ₹91
  37. 37.If 2 kites cost ₹50, how much do 11 kites cost? (a) ₹550 (b) ₹300 (c) ₹275 (d) ₹59
  38. 38.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹173 (b) ₹215 (c) ₹43 (d) ₹172
  39. 39.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 15 days (c) 16 days (d) 13 days
  40. 40.8 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 20 days

Answer key

  1. ₹40
  2. ₹250
  3. ₹60
  4. 26 days
  5. ₹56
  6. 7 days
  7. ₹228
  8. ₹80
  9. 10 days
  10. ₹150
  11. ₹45
  12. ₹217
  13. ₹42
  14. ₹12
  15. ₹27
  16. ₹70
  17. ₹80
  18. 8 days
  19. ₹96
  20. ₹21
  21. ₹216
  22. ₹56
  23. ₹21
  24. 7 days
  25. ₹76
  26. ₹45
  27. 3 days
  28. 5 days
  29. ₹20
  30. ₹36
  31. ₹63
  32. 9 days
  33. 6 days
  34. 5 days
  35. ₹198
  36. ₹91
  37. ₹275
  38. ₹172
  39. 16 days
  40. 20 days

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