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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 701 · 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 5 mangoes cost ₹30, how much do 6 mangoes cost? (a) ₹180 (b) ₹42 (c) ₹36 (d) ₹31
  2. 2.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 2 days (d) 3 days
  3. 3.If 8 pens cost ₹56, how much do 12 pens cost? (a) ₹91 (b) ₹672 (c) ₹84 (d) ₹60
  4. 4.If 7 mangoes cost ₹84, how much do 4 mangoes cost? (a) ₹81 (b) ₹336 (c) ₹48 (d) ₹60
  5. 5.If 4 kites cost ₹12, how much do 8 kites cost? (a) ₹27 (b) ₹16 (c) ₹24 (d) ₹96
  6. 6.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 14 days (d) 19 days
  7. 7.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 10 days (d) 4 days
  8. 8.If 9 notebooks cost ₹90, how much do 2 notebooks cost? (a) ₹180 (b) ₹83 (c) ₹20 (d) ₹30
  9. 9.If 8 notebooks cost ₹136, how much do 7 notebooks cost? (a) ₹119 (b) ₹952 (c) ₹136 (d) ₹135
  10. 10.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 64 days (d) 63 days
  11. 11.If 3 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹264 (b) ₹96 (c) ₹88 (d) ₹32
  12. 12.If 6 kites cost ₹108, how much do 4 kites cost? (a) ₹90 (b) ₹432 (c) ₹106 (d) ₹72
  13. 13.If 9 kites cost ₹63, how much do 7 kites cost? (a) ₹441 (b) ₹56 (c) ₹49 (d) ₹61
  14. 14.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹25 (c) ₹30 (d) ₹5
  15. 15.₹387 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹215 (d) ₹258
  16. 16.If 7 notebooks cost ₹175, how much do 4 notebooks cost? (a) ₹125 (b) ₹700 (c) ₹100 (d) ₹172
  17. 17.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹91 (d) ₹79
  18. 18.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 17 days (d) 13 days
  19. 19.If 5 mangoes cost ₹25, how much do 9 mangoes cost? (a) ₹225 (b) ₹50 (c) ₹45 (d) ₹29
  20. 20.If 7 mangoes cost ₹28, how much do 2 mangoes cost? (a) ₹56 (b) ₹8 (c) ₹12 (d) ₹23
  21. 21.If 2 notebooks cost ₹12, how much do 12 notebooks cost? (a) ₹144 (b) ₹22 (c) ₹78 (d) ₹72
  22. 22.If 6 pens cost ₹24, how much do 5 pens cost? (a) ₹20 (b) ₹120 (c) ₹23 (d) ₹24
  23. 23.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹30 (d) ₹10
  24. 24.If 6 kites cost ₹24, how much do 9 kites cost? (a) ₹216 (b) ₹36 (c) ₹40 (d) ₹27
  25. 25.If 8 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹9 (b) ₹12 (c) ₹72 (d) ₹19
  26. 26.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 3 days
  27. 27.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 3 days (d) 4 days
  28. 28.5 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) 5 days (d) 4 days
  29. 29.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 39 days (d) 17 days
  30. 30.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 10 days (d) 16 days
  31. 31.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
  32. 32.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹198 (b) ₹72 (c) ₹324 (d) ₹36
  33. 33.If 3 pens cost ₹27, how much do 5 pens cost? (a) ₹54 (b) ₹135 (c) ₹29 (d) ₹45
  34. 34.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹66 (b) ₹12 (c) ₹72 (d) ₹60
  35. 35.If 4 notebooks cost ₹60, how much do 9 notebooks cost? (a) ₹135 (b) ₹540 (c) ₹150 (d) ₹65
  36. 36.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 7 days (d) 5 days
  37. 37.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹187 (b) ₹238 (c) ₹136 (d) ₹34
  38. 38.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
  39. 39.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 35 days (c) 15 days (d) 5 days
  40. 40.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 19 days (d) 36 days

Answer key

  1. ₹36
  2. 3 days
  3. ₹84
  4. ₹48
  5. ₹24
  6. 18 days
  7. 4 days
  8. ₹20
  9. ₹119
  10. 63 days
  11. ₹88
  12. ₹72
  13. ₹49
  14. ₹25
  15. ₹215
  16. ₹100
  17. ₹78
  18. 9 days
  19. ₹45
  20. ₹8
  21. ₹72
  22. ₹20
  23. ₹30
  24. ₹36
  25. ₹9
  26. 21 days
  27. 3 days
  28. 5 days
  29. 39 days
  30. 16 days
  31. 25 days
  32. ₹324
  33. ₹45
  34. ₹72
  35. ₹135
  36. 6 days
  37. ₹238
  38. 3 days
  39. 35 days
  40. 35 days

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