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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 911 · 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.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹143 (b) ₹22 (c) ₹110 (d) ₹176
  2. 2.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 12 days (d) 17 days
  3. 3.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
  4. 4.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹49 (b) ₹441 (c) ₹245 (d) ₹392
  5. 5.If 9 pens cost ₹27, how much do 2 pens cost? (a) ₹9 (b) ₹54 (c) ₹6 (d) ₹20
  6. 6.If 2 kites cost ₹32, how much do 3 kites cost? (a) ₹96 (b) ₹64 (c) ₹33 (d) ₹48
  7. 7.If 6 mangoes cost ₹54, how much do 9 mangoes cost? (a) ₹90 (b) ₹57 (c) ₹81 (d) ₹486
  8. 8.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 12 days (d) 13 days
  9. 9.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 4 days (d) 9 days
  10. 10.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 12 days (d) 9 days
  11. 11.If 9 pens cost ₹189, how much do 3 pens cost? (a) ₹567 (b) ₹63 (c) ₹84 (d) ₹183
  12. 12.If 5 mangoes cost ₹100, how much do 12 mangoes cost? (a) ₹260 (b) ₹240 (c) ₹1200 (d) ₹107
  13. 13.If 7 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹51 (b) ₹16 (c) ₹112 (d) ₹24
  14. 14.9 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) 30 days (d) 4 days
  15. 15.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹119 (d) ₹103
  16. 16.₹165 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹15 (b) ₹120 (c) ₹45 (d) ₹135
  17. 17.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 8 days
  18. 18.If 4 kites cost ₹32, how much do 9 kites cost? (a) ₹72 (b) ₹80 (c) ₹37 (d) ₹288
  19. 19.If 2 mangoes cost ₹46, how much do 4 mangoes cost? (a) ₹184 (b) ₹92 (c) ₹115 (d) ₹48
  20. 20.If 6 pens cost ₹108, how much do 4 pens cost? (a) ₹432 (b) ₹90 (c) ₹106 (d) ₹72
  21. 21.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 6 days (d) 18 days
  22. 22.If 8 notebooks cost ₹160, how much do 5 notebooks cost? (a) ₹800 (b) ₹100 (c) ₹120 (d) ₹157
  23. 23.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹160 (c) ₹16 (d) ₹144
  24. 24.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹27 (b) ₹30 (c) ₹25 (d) ₹216
  25. 25.If 9 kites cost ₹108, how much do 10 kites cost? (a) ₹132 (b) ₹109 (c) ₹1080 (d) ₹120
  26. 26.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 15 days (d) 13 days
  27. 27.If 2 kites cost ₹12, how much do 5 kites cost? (a) ₹15 (b) ₹60 (c) ₹36 (d) ₹30
  28. 28.If 3 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹66 (b) ₹198 (c) ₹26 (d) ₹72
  29. 29.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 3 days (d) 7 days
  30. 30.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 39 days (d) 40 days
  31. 31.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 11 days (d) 16 days
  32. 32.If 9 pens cost ₹90, how much do 7 pens cost? (a) ₹70 (b) ₹630 (c) ₹88 (d) ₹80
  33. 33.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
  34. 34.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹441 (b) ₹393 (c) ₹49 (d) ₹392
  35. 35.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 18 days (d) 12 days
  36. 36.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 24 days (b) 8 days (c) 6 days (d) 16 days
  37. 37.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹72 (d) ₹40
  38. 38.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹81 (d) ₹9
  39. 39.If 3 mangoes cost ₹9, how much do 4 mangoes cost? (a) ₹36 (b) ₹15 (c) ₹10 (d) ₹12
  40. 40.If 6 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹72 (b) ₹12 (c) ₹21 (d) ₹16

Answer key

  1. ₹176
  2. 16 days
  3. 3 days
  4. ₹392
  5. ₹6
  6. ₹48
  7. ₹81
  8. 12 days
  9. 9 days
  10. 8 days
  11. ₹63
  12. ₹240
  13. ₹16
  14. 30 days
  15. ₹102
  16. ₹120
  17. 7 days
  18. ₹72
  19. ₹92
  20. ₹72
  21. 6 days
  22. ₹100
  23. ₹144
  24. ₹27
  25. ₹120
  26. 15 days
  27. ₹30
  28. ₹66
  29. 7 days
  30. 39 days
  31. 15 days
  32. ₹70
  33. 4 days
  34. ₹392
  35. 2 days
  36. 6 days
  37. ₹72
  38. ₹81
  39. ₹12
  40. ₹12

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