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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 815 · 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 4 pens cost ₹24, how much do 5 pens cost? (a) ₹36 (b) ₹25 (c) ₹30 (d) ₹120
  2. 2.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 19 days (d) 49 days
  3. 3.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 6 days (d) 8 days
  4. 4.If 9 mangoes cost ₹99, how much do 6 mangoes cost? (a) ₹77 (b) ₹66 (c) ₹96 (d) ₹594
  5. 5.If 5 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹41 (b) ₹240 (c) ₹48 (d) ₹56
  6. 6.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 18 days (c) 28 days (d) 10 days
  7. 7.If 7 pens cost ₹147, how much do 2 pens cost? (a) ₹294 (b) ₹63 (c) ₹42 (d) ₹142
  8. 8.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 3 days
  9. 9.If 3 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹270 (b) ₹100 (c) ₹90 (d) ₹36
  10. 10.If 5 kites cost ₹100, how much do 2 kites cost? (a) ₹60 (b) ₹200 (c) ₹97 (d) ₹40
  11. 11.If 8 kites cost ₹96, how much do 9 kites cost? (a) ₹864 (b) ₹120 (c) ₹97 (d) ₹108
  12. 12.If 7 notebooks cost ₹154, how much do 12 notebooks cost? (a) ₹159 (b) ₹1848 (c) ₹264 (d) ₹286
  13. 13.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 4 days (d) 3 days
  14. 14.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹60 (b) ₹108 (c) ₹120 (d) ₹12
  15. 15.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
  16. 16.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹40 (c) ₹240 (d) ₹280
  17. 17.If 4 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹29 (c) ₹54 (d) ₹60
  18. 18.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹40 (c) ₹48 (d) ₹44
  19. 19.If 5 mangoes cost ₹95, how much do 3 mangoes cost? (a) ₹93 (b) ₹57 (c) ₹285 (d) ₹76
  20. 20.If 7 mangoes cost ₹98, how much do 10 mangoes cost? (a) ₹140 (b) ₹154 (c) ₹980 (d) ₹101
  21. 21.If 2 mangoes cost ₹16, how much do 8 mangoes cost? (a) ₹22 (b) ₹64 (c) ₹72 (d) ₹128
  22. 22.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
  23. 23.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹81 (b) ₹55 (c) ₹27 (d) ₹54
  24. 24.₹352 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹176 (b) ₹160 (c) ₹192 (d) ₹32
  25. 25.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 3 days (c) 36 days (d) 15 days
  26. 26.If 5 notebooks cost ₹80, how much do 3 notebooks cost? (a) ₹240 (b) ₹64 (c) ₹78 (d) ₹48
  27. 27.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹390 (b) ₹195 (c) ₹351 (d) ₹39
  28. 28.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹72 (b) ₹144 (c) ₹96 (d) ₹49
  29. 29.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹126 (b) ₹90 (c) ₹18 (d) ₹108
  30. 30.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 5 days
  31. 31.If 2 pens cost ₹38, how much do 3 pens cost? (a) ₹39 (b) ₹57 (c) ₹76 (d) ₹114
  32. 32.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹87 (c) ₹129 (d) ₹86
  33. 33.If 8 mangoes cost ₹200, how much do 11 mangoes cost? (a) ₹2200 (b) ₹300 (c) ₹203 (d) ₹275
  34. 34.If 2 mangoes cost ₹40, how much do 4 mangoes cost? (a) ₹160 (b) ₹80 (c) ₹42 (d) ₹100
  35. 35.If 6 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹40 (b) ₹57 (c) ₹180 (d) ₹30
  36. 36.If 4 notebooks cost ₹32, how much do 10 notebooks cost? (a) ₹38 (b) ₹80 (c) ₹320 (d) ₹88
  37. 37.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 45 days (d) 21 days
  38. 38.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹200 (b) ₹240 (c) ₹40 (d) ₹280
  39. 39.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 19 days (d) 12 days
  40. 40.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹6 (d) ₹15

Answer key

  1. ₹30
  2. 49 days
  3. 7 days
  4. ₹66
  5. ₹48
  6. 7 days
  7. ₹42
  8. 7 days
  9. ₹90
  10. ₹40
  11. ₹108
  12. ₹264
  13. 3 days
  14. ₹108
  15. 28 days
  16. ₹240
  17. ₹54
  18. ₹48
  19. ₹57
  20. ₹140
  21. ₹64
  22. 3 days
  23. ₹54
  24. ₹192
  25. 36 days
  26. ₹48
  27. ₹351
  28. ₹72
  29. ₹126
  30. 7 days
  31. ₹57
  32. ₹86
  33. ₹275
  34. ₹80
  35. ₹30
  36. ₹80
  37. 5 days
  38. ₹280
  39. 18 days
  40. ₹18

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