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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 975 · 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. 1.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 11 days
  2. 2.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 40 days (c) 20 days (d) 41 days
  3. 3.If 2 pens cost ₹30, how much do 5 pens cost? (a) ₹90 (b) ₹33 (c) ₹75 (d) ₹150
  4. 4.If 2 kites cost ₹10, how much do 5 kites cost? (a) ₹50 (b) ₹25 (c) ₹13 (d) ₹30
  5. 5.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹264 (b) ₹44 (c) ₹220 (d) ₹242
  6. 6.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹16 (b) ₹96 (c) ₹80 (d) ₹112
  7. 7.If 3 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹162 (b) ₹59 (c) ₹144 (d) ₹432
  8. 8.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 35 days (d) 36 days
  9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 26 days (c) 11 days (d) 27 days
  10. 10.If 3 kites cost ₹27, how much do 6 kites cost? (a) ₹63 (b) ₹54 (c) ₹162 (d) ₹30
  11. 11.If 3 pens cost ₹30, how much do 9 pens cost? (a) ₹90 (b) ₹100 (c) ₹36 (d) ₹270
  12. 12.₹105 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹60 (b) ₹15 (c) ₹45 (d) ₹75
  13. 13.5 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
  14. 14.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 4 days (d) 19 days
  15. 15.₹81 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹18 (b) ₹72 (c) ₹63 (d) ₹9
  16. 16.₹390 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹120 (b) ₹195 (c) ₹270 (d) ₹30
  17. 17.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 2 days (c) 19 days (d) 12 days
  18. 18.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 1 day (d) 8 days
  19. 19.If 4 notebooks cost ₹96, how much do 10 notebooks cost? (a) ₹264 (b) ₹240 (c) ₹960 (d) ₹102
  20. 20.7 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
  21. 21.If 4 kites cost ₹52, how much do 8 kites cost? (a) ₹416 (b) ₹117 (c) ₹104 (d) ₹56
  22. 22.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹390 (c) ₹351 (d) ₹39
  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) 9 days (c) 6 days (d) 8 days
  24. 24.If 2 kites cost ₹16, how much do 6 kites cost? (a) ₹56 (b) ₹48 (c) ₹96 (d) ₹20
  25. 25.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 19 days (c) 11 days (d) 27 days
  26. 26.If 8 mangoes cost ₹200, how much do 5 mangoes cost? (a) ₹125 (b) ₹150 (c) ₹1000 (d) ₹197
  27. 27.₹51 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹17 (b) ₹51 (c) ₹34 (d) ₹35
  28. 28.If 6 notebooks cost ₹120, how much do 4 notebooks cost? (a) ₹100 (b) ₹480 (c) ₹118 (d) ₹80
  29. 29.If 3 mangoes cost ₹39, how much do 7 mangoes cost? (a) ₹104 (b) ₹273 (c) ₹43 (d) ₹91
  30. 30.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹216 (b) ₹243 (c) ₹81 (d) ₹27
  31. 31.If 6 pens cost ₹78, how much do 5 pens cost? (a) ₹77 (b) ₹78 (c) ₹65 (d) ₹390
  32. 32.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 17 days (d) 39 days
  33. 33.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹144 (c) ₹180 (d) ₹36
  34. 34.₹25 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹5 (c) ₹21 (d) ₹25
  35. 35.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 3 days (d) 1 day
  36. 36.If 8 pens cost ₹72, how much do 6 pens cost? (a) ₹54 (b) ₹432 (c) ₹70 (d) ₹63
  37. 37.If 9 mangoes cost ₹225, how much do 2 mangoes cost? (a) ₹450 (b) ₹75 (c) ₹218 (d) ₹50
  38. 38.If 4 pens cost ₹56, how much do 3 pens cost? (a) ₹56 (b) ₹168 (c) ₹55 (d) ₹42
  39. 39.If 3 mangoes cost ₹15, how much do 10 mangoes cost? (a) ₹22 (b) ₹150 (c) ₹55 (d) ₹50
  40. 40.If 3 pens cost ₹12, how much do 10 pens cost? (a) ₹44 (b) ₹40 (c) ₹120 (d) ₹19

Answer key

  1. 10 days
  2. 40 days
  3. ₹75
  4. ₹25
  5. ₹264
  6. ₹112
  7. ₹144
  8. 35 days
  9. 26 days
  10. ₹54
  11. ₹90
  12. ₹60
  13. 5 days
  14. 49 days
  15. ₹63
  16. ₹270
  17. 18 days
  18. 2 days
  19. ₹240
  20. 7 days
  21. ₹104
  22. ₹351
  23. 8 days
  24. ₹48
  25. 27 days
  26. ₹125
  27. ₹34
  28. ₹80
  29. ₹91
  30. ₹216
  31. ₹65
  32. 39 days
  33. ₹180
  34. ₹20
  35. 3 days
  36. ₹54
  37. ₹50
  38. ₹42
  39. ₹50
  40. ₹40

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