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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 388 · 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 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
  2. 2.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 5 days
  3. 3.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 10 days
  4. 4.If 8 pens cost ₹128, how much do 2 pens cost? (a) ₹256 (b) ₹48 (c) ₹32 (d) ₹122
  5. 5.If 7 pens cost ₹21, how much do 12 pens cost? (a) ₹26 (b) ₹39 (c) ₹252 (d) ₹36
  6. 6.If 4 notebooks cost ₹16, how much do 3 notebooks cost? (a) ₹16 (b) ₹15 (c) ₹48 (d) ₹12
  7. 7.If 4 notebooks cost ₹88, how much do 11 notebooks cost? (a) ₹95 (b) ₹242 (c) ₹264 (d) ₹968
  8. 8.₹192 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹168 (b) ₹96 (c) ₹24 (d) ₹192
  9. 9.₹360 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹108 (d) ₹252
  10. 10.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 10 days (c) 18 days (d) 43 days
  11. 11.If 8 mangoes cost ₹64, how much do 7 mangoes cost? (a) ₹448 (b) ₹56 (c) ₹64 (d) ₹63
  12. 12.If 8 pens cost ₹40, how much do 7 pens cost? (a) ₹280 (b) ₹40 (c) ₹35 (d) ₹39
  13. 13.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 36 days (b) 20 days (c) 4 days (d) 5 days
  14. 14.₹78 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹39 (c) ₹48 (d) ₹6
  15. 15.If 4 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹75 (b) ₹90 (c) ₹61 (d) ₹300
  16. 16.5 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 21 days (d) 20 days
  17. 17.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 12 days (d) 8 days
  18. 18.If 2 kites cost ₹14, how much do 12 kites cost? (a) ₹168 (b) ₹24 (c) ₹84 (d) ₹91
  19. 19.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 18 days (d) 19 days
  20. 20.If 4 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹73 (b) ₹108 (c) ₹90 (d) ₹360
  21. 21.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 14 days (d) 5 days
  22. 22.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 22 days (d) 23 days
  23. 23.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹110 (b) ₹66 (c) ₹22 (d) ₹154
  24. 24.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹120 (b) ₹84 (c) ₹48 (d) ₹24
  25. 25.If 2 notebooks cost ₹28, how much do 4 notebooks cost? (a) ₹70 (b) ₹112 (c) ₹30 (d) ₹56
  26. 26.If 5 notebooks cost ₹85, how much do 2 notebooks cost? (a) ₹34 (b) ₹170 (c) ₹51 (d) ₹82
  27. 27.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 15 days (d) 13 days
  28. 28.If 8 pens cost ₹56, how much do 7 pens cost? (a) ₹56 (b) ₹55 (c) ₹392 (d) ₹49
  29. 29.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 12 days (c) 19 days (d) 18 days
  30. 30.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹56 (d) ₹48
  31. 31.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹56 (d) ₹28
  32. 32.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 27 days (c) 17 days (d) 3 days
  33. 33.If 3 notebooks cost ₹75, how much do 6 notebooks cost? (a) ₹150 (b) ₹78 (c) ₹450 (d) ₹175
  34. 34.If 6 pens cost ₹42, how much do 11 pens cost? (a) ₹84 (b) ₹462 (c) ₹47 (d) ₹77
  35. 35.If 8 mangoes cost ₹152, how much do 12 mangoes cost? (a) ₹156 (b) ₹1824 (c) ₹247 (d) ₹228
  36. 36.If 3 kites cost ₹24, how much do 10 kites cost? (a) ₹31 (b) ₹88 (c) ₹80 (d) ₹240
  37. 37.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
  38. 38.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹369 (b) ₹41 (c) ₹164 (d) ₹410
  39. 39.₹440 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹44 (b) ₹132 (c) ₹308 (d) ₹220
  40. 40.If 3 notebooks cost ₹9, how much do 6 notebooks cost? (a) ₹18 (b) ₹21 (c) ₹12 (d) ₹54

Answer key

  1. 39 days
  2. 6 days
  3. 4 days
  4. ₹32
  5. ₹36
  6. ₹12
  7. ₹242
  8. ₹168
  9. ₹252
  10. 42 days
  11. ₹56
  12. ₹35
  13. 4 days
  14. ₹48
  15. ₹75
  16. 20 days
  17. 12 days
  18. ₹84
  19. 18 days
  20. ₹90
  21. 5 days
  22. 22 days
  23. ₹154
  24. ₹120
  25. ₹56
  26. ₹34
  27. 14 days
  28. ₹49
  29. 18 days
  30. ₹64
  31. ₹42
  32. 3 days
  33. ₹150
  34. ₹77
  35. ₹228
  36. ₹80
  37. 21 days
  38. ₹369
  39. ₹308
  40. ₹18

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