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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 920 · 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 3 pens cost ₹45, how much do 2 pens cost? (a) ₹44 (b) ₹90 (c) ₹30 (d) ₹45
  2. 2.If 3 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹192 (b) ₹528 (c) ₹176 (d) ₹56
  3. 3.If 2 notebooks cost ₹42, how much do 11 notebooks cost? (a) ₹51 (b) ₹462 (c) ₹231 (d) ₹252
  4. 4.If 2 pens cost ₹50, how much do 4 pens cost? (a) ₹125 (b) ₹200 (c) ₹52 (d) ₹100
  5. 5.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 22 days (d) 11 days
  6. 6.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 56 days (c) 20 days (d) 57 days
  7. 7.If 3 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹110 (b) ₹67 (c) ₹264 (d) ₹88
  8. 8.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 44 days (c) 5 days (d) 17 days
  9. 9.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 15 days
  10. 10.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
  11. 11.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹259 (b) ₹222 (c) ₹37 (d) ₹185
  12. 12.₹351 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹313 (b) ₹312 (c) ₹39 (d) ₹351
  13. 13.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹60 (b) ₹30 (c) ₹21 (d) ₹40
  14. 14.If 9 mangoes cost ₹216, how much do 2 mangoes cost? (a) ₹48 (b) ₹209 (c) ₹72 (d) ₹432
  15. 15.If 8 mangoes cost ₹128, how much do 12 mangoes cost? (a) ₹132 (b) ₹1536 (c) ₹208 (d) ₹192
  16. 16.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹27 (d) ₹36
  17. 17.If 2 mangoes cost ₹22, how much do 7 mangoes cost? (a) ₹27 (b) ₹88 (c) ₹77 (d) ₹154
  18. 18.If 2 kites cost ₹30, how much do 3 kites cost? (a) ₹60 (b) ₹31 (c) ₹90 (d) ₹45
  19. 19.If 6 kites cost ₹24, how much do 2 kites cost? (a) ₹8 (b) ₹20 (c) ₹48 (d) ₹12
  20. 20.If 2 mangoes cost ₹28, how much do 6 mangoes cost? (a) ₹98 (b) ₹84 (c) ₹32 (d) ₹168
  21. 21.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹264 (b) ₹44 (c) ₹308 (d) ₹154
  22. 22.If 3 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹48 (b) ₹270 (c) ₹105 (d) ₹90
  23. 23.₹297 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹264 (b) ₹231 (c) ₹66 (d) ₹33
  24. 24.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹7 (c) ₹35 (d) ₹49
  25. 25.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹152 (b) ₹133 (c) ₹76 (d) ₹19
  26. 26.If 7 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹36 (b) ₹80 (c) ₹252 (d) ₹48
  27. 27.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 17 days (c) 13 days (d) 22 days
  28. 28.If 9 kites cost ₹180, how much do 5 kites cost? (a) ₹176 (b) ₹900 (c) ₹100 (d) ₹120
  29. 29.If 6 kites cost ₹72, how much do 8 kites cost? (a) ₹108 (b) ₹576 (c) ₹74 (d) ₹96
  30. 30.If 2 pens cost ₹16, how much do 5 pens cost? (a) ₹80 (b) ₹19 (c) ₹48 (d) ₹40
  31. 31.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹55 (b) ₹81 (c) ₹54 (d) ₹27
  32. 32.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹225 (b) ₹45 (c) ₹315 (d) ₹270
  33. 33.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 17 days (d) 11 days
  34. 34.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 6 days (d) 21 days
  35. 35.₹60 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹6 (b) ₹30 (c) ₹18 (d) ₹42
  36. 36.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 3 days (d) 6 days
  37. 37.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 11 days
  38. 38.If 2 kites cost ₹10, how much do 12 kites cost? (a) ₹120 (b) ₹20 (c) ₹65 (d) ₹60
  39. 39.₹162 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹18 (b) ₹81 (c) ₹126 (d) ₹36
  40. 40.If 7 pens cost ₹133, how much do 10 pens cost? (a) ₹136 (b) ₹1330 (c) ₹209 (d) ₹190

Answer key

  1. ₹30
  2. ₹176
  3. ₹231
  4. ₹100
  5. 21 days
  6. 56 days
  7. ₹88
  8. 44 days
  9. 21 days
  10. 45 days
  11. ₹259
  12. ₹312
  13. ₹30
  14. ₹48
  15. ₹192
  16. ₹36
  17. ₹77
  18. ₹45
  19. ₹8
  20. ₹84
  21. ₹264
  22. ₹90
  23. ₹231
  24. ₹42
  25. ₹133
  26. ₹36
  27. 21 days
  28. ₹100
  29. ₹96
  30. ₹40
  31. ₹54
  32. ₹315
  33. 12 days
  34. 6 days
  35. ₹42
  36. 7 days
  37. 5 days
  38. ₹60
  39. ₹126
  40. ₹190

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