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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 324 · 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. 1.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 3 days (d) 10 days
  2. 2.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 9 days (d) 8 days
  3. 3.₹200 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹20 (b) ₹200 (c) ₹100 (d) ₹180
  4. 4.₹54 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹6 (b) ₹54 (c) ₹27 (d) ₹48
  5. 5.If 6 mangoes cost ₹90, how much do 3 mangoes cost? (a) ₹270 (b) ₹87 (c) ₹60 (d) ₹45
  6. 6.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 12 days (d) 13 days
  7. 7.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹27 (d) ₹36
  8. 8.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 26 days (c) 9 days (d) 27 days
  9. 9.If 4 kites cost ₹32, how much do 12 kites cost? (a) ₹104 (b) ₹384 (c) ₹96 (d) ₹40
  10. 10.If 9 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹39 (b) ₹48 (c) ₹432 (d) ₹52
  11. 11.If 5 kites cost ₹80, how much do 6 kites cost? (a) ₹112 (b) ₹81 (c) ₹96 (d) ₹480
  12. 12.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 3 days
  13. 13.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 15 days (c) 6 days (d) 7 days
  14. 14.If 8 pens cost ₹80, how much do 9 pens cost? (a) ₹81 (b) ₹90 (c) ₹100 (d) ₹720
  15. 15.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 16 days (c) 41 days (d) 4 days
  16. 16.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 6 days (d) 7 days
  17. 17.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 21 days (d) 22 days
  18. 18.If 4 kites cost ₹16, how much do 11 kites cost? (a) ₹23 (b) ₹48 (c) ₹176 (d) ₹44
  19. 19.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 15 days (d) 14 days
  20. 20.If 2 pens cost ₹18, how much do 11 pens cost? (a) ₹27 (b) ₹198 (c) ₹99 (d) ₹108
  21. 21.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 6 days (d) 20 days
  22. 22.If 8 pens cost ₹160, how much do 4 pens cost? (a) ₹640 (b) ₹156 (c) ₹100 (d) ₹80
  23. 23.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹147 (d) ₹392
  24. 24.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 17 days (c) 5 days (d) 4 days
  25. 25.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 13 days
  26. 26.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 5 days (d) 15 days
  27. 27.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 1 day (d) 4 days
  28. 28.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹60 (d) ₹42
  29. 29.₹135 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹15 (d) ₹75
  30. 30.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 5 days (d) 20 days
  31. 31.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 24 days (c) 25 days (d) 18 days
  32. 32.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹195 (b) ₹351 (c) ₹390 (d) ₹39
  33. 33.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 56 days (c) 8 days (d) 57 days
  34. 34.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹112 (c) ₹28 (d) ₹126
  35. 35.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 31 days (b) 16 days (c) 4 days (d) 30 days
  36. 36.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹350 (c) ₹250 (d) ₹300
  37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
  38. 38.If 8 mangoes cost ₹144, how much do 7 mangoes cost? (a) ₹126 (b) ₹143 (c) ₹1008 (d) ₹144
  39. 39.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 17 days (d) 33 days
  40. 40.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 2 days

Answer key

  1. 9 days
  2. 9 days
  3. ₹180
  4. ₹48
  5. ₹45
  6. 12 days
  7. ₹36
  8. 26 days
  9. ₹96
  10. ₹48
  11. ₹96
  12. 14 days
  13. 7 days
  14. ₹90
  15. 40 days
  16. 6 days
  17. 21 days
  18. ₹44
  19. 14 days
  20. ₹99
  21. 5 days
  22. ₹80
  23. ₹392
  24. 5 days
  25. 5 days
  26. 35 days
  27. 3 days
  28. ₹60
  29. ₹75
  30. 20 days
  31. 24 days
  32. ₹351
  33. 56 days
  34. ₹140
  35. 30 days
  36. ₹350
  37. 3 days
  38. ₹126
  39. 33 days
  40. 3 days

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