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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 275 · 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. 1.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
  2. 2.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 1 day (d) 12 days
  3. 3.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹54 (c) ₹72 (d) ₹108
  4. 4.If 3 kites cost ₹66, how much do 12 kites cost? (a) ₹75 (b) ₹264 (c) ₹286 (d) ₹792
  5. 5.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹126 (b) ₹140 (c) ₹112 (d) ₹28
  6. 6.₹135 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹109 (d) ₹135
  7. 7.If 8 mangoes cost ₹200, how much do 9 mangoes cost? (a) ₹201 (b) ₹250 (c) ₹1800 (d) ₹225
  8. 8.If 5 kites cost ₹60, how much do 12 kites cost? (a) ₹720 (b) ₹144 (c) ₹67 (d) ₹156
  9. 9.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹30 (d) ₹35
  10. 10.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 15 days (d) 14 days
  11. 11.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹80 (d) ₹48
  12. 12.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
  13. 13.If 8 pens cost ₹72, how much do 4 pens cost? (a) ₹45 (b) ₹36 (c) ₹288 (d) ₹68
  14. 14.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹276 (d) ₹230
  15. 15.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 5 days (d) 13 days
  16. 16.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 3 days (d) 5 days
  17. 17.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹253 (d) ₹322
  18. 18.₹132 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹77 (d) ₹66
  19. 19.If 9 pens cost ₹180, how much do 3 pens cost? (a) ₹80 (b) ₹174 (c) ₹540 (d) ₹60
  20. 20.If 6 pens cost ₹18, how much do 11 pens cost? (a) ₹23 (b) ₹36 (c) ₹198 (d) ₹33
  21. 21.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 9 days (d) 19 days
  22. 22.If 2 notebooks cost ₹16, how much do 9 notebooks cost? (a) ₹72 (b) ₹23 (c) ₹144 (d) ₹80
  23. 23.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 9 days
  24. 24.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 9 days (d) 17 days
  25. 25.6 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 24 days (c) 6 days (d) 7 days
  26. 26.If 6 kites cost ₹48, how much do 11 kites cost? (a) ₹88 (b) ₹528 (c) ₹96 (d) ₹53
  27. 27.₹564 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹235 (b) ₹47 (c) ₹329 (d) ₹282
  28. 28.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 4 days (d) 16 days
  29. 29.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 5 days (d) 4 days
  30. 30.If 8 kites cost ₹40, how much do 6 kites cost? (a) ₹30 (b) ₹38 (c) ₹35 (d) ₹240
  31. 31.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹150 (b) ₹195 (c) ₹30 (d) ₹240
  32. 32.If 8 kites cost ₹24, how much do 4 kites cost? (a) ₹20 (b) ₹15 (c) ₹96 (d) ₹12
  33. 33.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹42 (d) ₹49
  34. 34.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 16 days (c) 14 days (d) 20 days
  35. 35.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹315 (b) ₹175 (c) ₹35 (d) ₹245
  36. 36.If 4 notebooks cost ₹12, how much do 7 notebooks cost? (a) ₹84 (b) ₹24 (c) ₹21 (d) ₹15
  37. 37.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 8 days (d) 7 days
  38. 38.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 12 days (d) 15 days
  39. 39.If 2 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹72 (b) ₹48 (c) ₹25 (d) ₹36
  40. 40.If 7 notebooks cost ₹63, how much do 6 notebooks cost? (a) ₹54 (b) ₹63 (c) ₹378 (d) ₹62

Answer key

  1. 25 days
  2. 3 days
  3. ₹72
  4. ₹264
  5. ₹140
  6. ₹108
  7. ₹225
  8. ₹144
  9. ₹35
  10. 14 days
  11. ₹80
  12. 5 days
  13. ₹36
  14. ₹322
  15. 27 days
  16. 4 days
  17. ₹322
  18. ₹77
  19. ₹60
  20. ₹33
  21. 7 days
  22. ₹72
  23. 8 days
  24. 8 days
  25. 6 days
  26. ₹88
  27. ₹329
  28. 30 days
  29. 5 days
  30. ₹30
  31. ₹240
  32. ₹12
  33. ₹42
  34. 20 days
  35. ₹315
  36. ₹21
  37. 2 days
  38. 14 days
  39. ₹36
  40. ₹54

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