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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 222 · 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 notebooks cost ₹25, how much do 6 notebooks cost? (a) ₹26 (b) ₹150 (c) ₹30 (d) ₹35
  2. 2.6 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) 5 days
  3. 3.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 14 days (d) 9 days
  4. 4.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 21 days (d) 22 days
  5. 5.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 11 days
  6. 6.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹35 (c) ₹63 (d) ₹49
  7. 7.If 3 pens cost ₹42, how much do 11 pens cost? (a) ₹50 (b) ₹168 (c) ₹154 (d) ₹462
  8. 8.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹252 (b) ₹231 (c) ₹42 (d) ₹210
  9. 9.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 43 days (d) 42 days
  10. 10.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹279 (b) ₹31 (c) ₹249 (d) ₹248
  11. 11.₹91 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹13 (d) ₹65
  12. 12.If 7 notebooks cost ₹63, how much do 3 notebooks cost? (a) ₹36 (b) ₹27 (c) ₹189 (d) ₹59
  13. 13.If 6 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹36 (b) ₹144 (c) ₹68 (d) ₹24
  14. 14.If 9 mangoes cost ₹189, how much do 7 mangoes cost? (a) ₹168 (b) ₹147 (c) ₹1323 (d) ₹187
  15. 15.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 15 days (d) 11 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) 7 days (d) 6 days
  17. 17.If 2 notebooks cost ₹22, how much do 5 notebooks cost? (a) ₹110 (b) ₹25 (c) ₹66 (d) ₹55
  18. 18.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹144 (d) ₹36
  19. 19.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 22 days (c) 8 days (d) 23 days
  20. 20.If 6 mangoes cost ₹126, how much do 2 mangoes cost? (a) ₹63 (b) ₹122 (c) ₹252 (d) ₹42
  21. 21.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 8 days (d) 3 days
  22. 22.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 18 days (c) 16 days (d) 8 days
  23. 23.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 32 days (c) 2 days (d) 14 days
  24. 24.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹45 (b) ₹75 (c) ₹60 (d) ₹15
  25. 25.If 2 kites cost ₹48, how much do 6 kites cost? (a) ₹168 (b) ₹288 (c) ₹144 (d) ₹52
  26. 26.If 9 pens cost ₹36, how much do 8 pens cost? (a) ₹35 (b) ₹288 (c) ₹32 (d) ₹36
  27. 27.₹396 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹324 (b) ₹198 (c) ₹72 (d) ₹36
  28. 28.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 7 days
  29. 29.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 27 days (d) 26 days
  30. 30.If 2 notebooks cost ₹24, how much do 12 notebooks cost? (a) ₹144 (b) ₹288 (c) ₹34 (d) ₹156
  31. 31.7 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) 14 days (d) 15 days
  32. 32.If 3 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹32 (b) ₹96 (c) ₹25 (d) ₹40
  33. 33.If 9 kites cost ₹54, how much do 8 kites cost? (a) ₹432 (b) ₹54 (c) ₹48 (d) ₹53
  34. 34.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 12 days (d) 2 days
  35. 35.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹9 (c) ₹36 (d) ₹54
  36. 36.If 7 pens cost ₹84, how much do 3 pens cost? (a) ₹48 (b) ₹252 (c) ₹80 (d) ₹36
  37. 37.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹6 (b) ₹42 (c) ₹33 (d) ₹24
  38. 38.If 9 mangoes cost ₹135, how much do 10 mangoes cost? (a) ₹150 (b) ₹165 (c) ₹1350 (d) ₹136
  39. 39.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹72 (d) ₹144
  40. 40.If 6 pens cost ₹54, how much do 11 pens cost? (a) ₹594 (b) ₹99 (c) ₹108 (d) ₹59

Answer key

  1. ₹30
  2. 6 days
  3. 8 days
  4. 21 days
  5. 6 days
  6. ₹63
  7. ₹154
  8. ₹252
  9. 42 days
  10. ₹248
  11. ₹65
  12. ₹27
  13. ₹24
  14. ₹147
  15. 15 days
  16. 6 days
  17. ₹55
  18. ₹144
  19. 22 days
  20. ₹42
  21. 12 days
  22. 8 days
  23. 32 days
  24. ₹75
  25. ₹144
  26. ₹32
  27. ₹324
  28. 4 days
  29. 26 days
  30. ₹144
  31. 14 days
  32. ₹32
  33. ₹48
  34. 3 days
  35. ₹45
  36. ₹36
  37. ₹42
  38. ₹150
  39. ₹120
  40. ₹99

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