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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 129 · 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. 1.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 12 days (d) 13 days
  2. 2.₹225 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹225 (b) ₹181 (c) ₹45 (d) ₹180
  3. 3.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 3 days (d) 1 day
  4. 4.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹322 (b) ₹46 (c) ₹184 (d) ₹368
  5. 5.If 7 notebooks cost ₹56, how much do 10 notebooks cost? (a) ₹560 (b) ₹59 (c) ₹88 (d) ₹80
  6. 6.If 2 pens cost ₹38, how much do 3 pens cost? (a) ₹76 (b) ₹39 (c) ₹114 (d) ₹57
  7. 7.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹161 (b) ₹230 (c) ₹46 (d) ₹92
  8. 8.If 6 notebooks cost ₹60, how much do 9 notebooks cost? (a) ₹90 (b) ₹540 (c) ₹100 (d) ₹63
  9. 9.If 8 notebooks cost ₹176, how much do 5 notebooks cost? (a) ₹132 (b) ₹880 (c) ₹110 (d) ₹173
  10. 10.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹23 (b) ₹115 (c) ₹138 (d) ₹161
  11. 11.If 6 kites cost ₹126, how much do 2 kites cost? (a) ₹252 (b) ₹42 (c) ₹122 (d) ₹63
  12. 12.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 11 days (d) 17 days
  13. 13.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹147 (b) ₹196 (c) ₹49 (d) ₹98
  14. 14.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 6 days
  15. 15.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹36 (c) ₹24 (d) ₹12
  16. 16.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹115 (b) ₹93 (c) ₹92 (d) ₹23
  17. 17.If 3 kites cost ₹18, how much do 7 kites cost? (a) ₹126 (b) ₹42 (c) ₹48 (d) ₹22
  18. 18.₹385 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹105 (b) ₹280 (c) ₹35 (d) ₹315
  19. 19.If 2 notebooks cost ₹10, how much do 12 notebooks cost? (a) ₹65 (b) ₹20 (c) ₹120 (d) ₹60
  20. 20.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹224 (d) ₹256
  21. 21.₹495 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹315 (c) ₹270 (d) ₹225
  22. 22.If 8 kites cost ₹128, how much do 12 kites cost? (a) ₹132 (b) ₹192 (c) ₹208 (d) ₹1536
  23. 23.If 6 kites cost ₹108, how much do 2 kites cost? (a) ₹104 (b) ₹54 (c) ₹36 (d) ₹216
  24. 24.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 5 days (d) 14 days
  25. 25.₹112 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹56 (b) ₹8 (c) ₹72 (d) ₹40
  26. 26.If 6 kites cost ₹18, how much do 4 kites cost? (a) ₹16 (b) ₹72 (c) ₹15 (d) ₹12
  27. 27.If 2 kites cost ₹32, how much do 3 kites cost? (a) ₹96 (b) ₹64 (c) ₹33 (d) ₹48
  28. 28.If 5 kites cost ₹20, how much do 8 kites cost? (a) ₹36 (b) ₹32 (c) ₹23 (d) ₹160
  29. 29.If 6 pens cost ₹114, how much do 5 pens cost? (a) ₹114 (b) ₹570 (c) ₹95 (d) ₹113
  30. 30.If 5 pens cost ₹100, how much do 3 pens cost? (a) ₹98 (b) ₹300 (c) ₹60 (d) ₹80
  31. 31.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹60 (d) ₹40
  32. 32.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 8 days (d) 7 days
  33. 33.If 6 kites cost ₹36, how much do 7 kites cost? (a) ₹42 (b) ₹37 (c) ₹252 (d) ₹48
  34. 34.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 11 days (d) 12 days
  35. 35.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 15 days (d) 14 days
  36. 36.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹63 (b) ₹36 (c) ₹18 (d) ₹90
  37. 37.If 5 mangoes cost ₹15, how much do 6 mangoes cost? (a) ₹90 (b) ₹18 (c) ₹16 (d) ₹21
  38. 38.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 4 days
  39. 39.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 2 days (d) 18 days
  40. 40.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 20 days (d) 13 days

Answer key

  1. 12 days
  2. ₹180
  3. 2 days
  4. ₹322
  5. ₹80
  6. ₹57
  7. ₹230
  8. ₹90
  9. ₹110
  10. ₹161
  11. ₹42
  12. 35 days
  13. ₹147
  14. 5 days
  15. ₹36
  16. ₹92
  17. ₹42
  18. ₹280
  19. ₹60
  20. ₹224
  21. ₹270
  22. ₹192
  23. ₹36
  24. 14 days
  25. ₹72
  26. ₹12
  27. ₹48
  28. ₹32
  29. ₹95
  30. ₹60
  31. ₹40
  32. 7 days
  33. ₹42
  34. 3 days
  35. 14 days
  36. ₹90
  37. ₹18
  38. 3 days
  39. 2 days
  40. 5 days

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