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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 337 · 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. 1.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 9 days (c) 15 days (d) 5 days
  2. 2.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 7 days (d) 6 days
  3. 3.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
  4. 4.If 3 notebooks cost ₹66, how much do 10 notebooks cost? (a) ₹660 (b) ₹242 (c) ₹73 (d) ₹220
  5. 5.If 4 mangoes cost ₹20, how much do 6 mangoes cost? (a) ₹22 (b) ₹30 (c) ₹35 (d) ₹120
  6. 6.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹44 (b) ₹99 (c) ₹154 (d) ₹22
  7. 7.If 4 kites cost ₹68, how much do 9 kites cost? (a) ₹612 (b) ₹73 (c) ₹153 (d) ₹170
  8. 8.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹72 (b) ₹12 (c) ₹36 (d) ₹60
  9. 9.If 5 kites cost ₹35, how much do 6 kites cost? (a) ₹49 (b) ₹36 (c) ₹42 (d) ₹210
  10. 10.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹33 (d) ₹66
  11. 11.If 2 kites cost ₹12, how much do 11 kites cost? (a) ₹66 (b) ₹132 (c) ₹72 (d) ₹21
  12. 12.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹20 (d) ₹40
  13. 13.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹135 (d) ₹120
  14. 14.If 9 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹360 (b) ₹68 (c) ₹40 (d) ₹48
  15. 15.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
  16. 16.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹110 (d) ₹120
  17. 17.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 36 days (c) 15 days (d) 1 day
  18. 18.If 8 pens cost ₹120, how much do 10 pens cost? (a) ₹150 (b) ₹165 (c) ₹1200 (d) ₹122
  19. 19.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
  20. 20.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 16 days (d) 15 days
  21. 21.₹203 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹116 (d) ₹145
  22. 22.₹182 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹91 (d) ₹78
  23. 23.If 4 kites cost ₹96, how much do 5 kites cost? (a) ₹120 (b) ₹97 (c) ₹480 (d) ₹144
  24. 24.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 4 days (d) 6 days
  25. 25.If 3 kites cost ₹15, how much do 8 kites cost? (a) ₹20 (b) ₹120 (c) ₹45 (d) ₹40
  26. 26.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹45 (d) ₹50
  27. 27.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹216 (c) ₹180 (d) ₹36
  28. 28.If 7 mangoes cost ₹140, how much do 12 mangoes cost? (a) ₹240 (b) ₹260 (c) ₹1680 (d) ₹145
  29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
  30. 30.₹42 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹21 (d) ₹28
  31. 31.If 5 notebooks cost ₹90, how much do 2 notebooks cost? (a) ₹87 (b) ₹180 (c) ₹36 (d) ₹54
  32. 32.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹65 (c) ₹91 (d) ₹78
  33. 33.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 15 days (d) 13 days
  34. 34.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
  35. 35.If 7 pens cost ₹21, how much do 11 pens cost? (a) ₹33 (b) ₹36 (c) ₹231 (d) ₹25
  36. 36.If 5 mangoes cost ₹70, how much do 11 mangoes cost? (a) ₹770 (b) ₹154 (c) ₹76 (d) ₹168
  37. 37.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹36 (b) ₹216 (c) ₹126 (d) ₹252
  38. 38.If 3 kites cost ₹33, how much do 4 kites cost? (a) ₹55 (b) ₹44 (c) ₹132 (d) ₹34
  39. 39.If 5 pens cost ₹65, how much do 6 pens cost? (a) ₹390 (b) ₹66 (c) ₹78 (d) ₹91
  40. 40.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 11 days (d) 28 days

Answer key

  1. 14 days
  2. 6 days
  3. 5 days
  4. ₹220
  5. ₹30
  6. ₹154
  7. ₹153
  8. ₹60
  9. ₹42
  10. ₹55
  11. ₹66
  12. ₹40
  13. ₹120
  14. ₹40
  15. 3 days
  16. ₹120
  17. 36 days
  18. ₹150
  19. 3 days
  20. 15 days
  21. ₹116
  22. ₹104
  23. ₹120
  24. 16 days
  25. ₹40
  26. ₹45
  27. ₹216
  28. ₹240
  29. 3 days
  30. ₹28
  31. ₹36
  32. ₹91
  33. 21 days
  34. 20 days
  35. ₹33
  36. ₹154
  37. ₹216
  38. ₹44
  39. ₹78
  40. 28 days

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