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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 138 · 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.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹72 (b) ₹16 (c) ₹64 (d) ₹80
  2. 2.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 8 days (d) 7 days
  3. 3.If 3 pens cost ₹27, how much do 11 pens cost? (a) ₹108 (b) ₹35 (c) ₹99 (d) ₹297
  4. 4.If 4 mangoes cost ₹16, how much do 11 mangoes cost? (a) ₹48 (b) ₹23 (c) ₹44 (d) ₹176
  5. 5.If 2 pens cost ₹20, how much do 8 pens cost? (a) ₹90 (b) ₹26 (c) ₹80 (d) ₹160
  6. 6.If 5 pens cost ₹50, how much do 8 pens cost? (a) ₹53 (b) ₹400 (c) ₹80 (d) ₹90
  7. 7.If 2 kites cost ₹48, how much do 7 kites cost? (a) ₹168 (b) ₹53 (c) ₹336 (d) ₹192
  8. 8.If 7 kites cost ₹105, how much do 10 kites cost? (a) ₹150 (b) ₹165 (c) ₹1050 (d) ₹108
  9. 9.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 17 days (c) 7 days (d) 6 days
  10. 10.If 4 pens cost ₹40, how much do 6 pens cost? (a) ₹240 (b) ₹42 (c) ₹60 (d) ₹70
  11. 11.If 2 pens cost ₹38, how much do 4 pens cost? (a) ₹40 (b) ₹76 (c) ₹152 (d) ₹95
  12. 12.If 4 pens cost ₹80, how much do 10 pens cost? (a) ₹86 (b) ₹200 (c) ₹800 (d) ₹220
  13. 13.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹333 (b) ₹297 (c) ₹296 (d) ₹37
  14. 14.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 11 days
  15. 15.₹560 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹280 (b) ₹360 (c) ₹200 (d) ₹40
  16. 16.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 13 days (d) 16 days
  17. 17.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 25 days (c) 4 days (d) 24 days
  18. 18.If 8 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹54 (b) ₹432 (c) ₹60 (d) ₹49
  19. 19.If 6 notebooks cost ₹54, how much do 7 notebooks cost? (a) ₹55 (b) ₹63 (c) ₹378 (d) ₹72
  20. 20.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹16 (b) ₹72 (c) ₹32 (d) ₹112
  21. 21.₹420 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹126 (d) ₹294
  22. 22.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹180 (b) ₹150 (c) ₹90 (d) ₹30
  23. 23.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 16 days (c) 10 days (d) 11 days
  24. 24.If 5 pens cost ₹105, how much do 11 pens cost? (a) ₹231 (b) ₹111 (c) ₹1155 (d) ₹252
  25. 25.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
  26. 26.If 6 pens cost ₹150, how much do 12 pens cost? (a) ₹300 (b) ₹156 (c) ₹325 (d) ₹1800
  27. 27.₹288 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹32 (b) ₹144 (c) ₹256 (d) ₹288
  28. 28.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹132 (d) ₹99
  29. 29.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 19 days (d) 13 days
  30. 30.If 3 pens cost ₹21, how much do 11 pens cost? (a) ₹29 (b) ₹84 (c) ₹77 (d) ₹231
  31. 31.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹11 (d) ₹44
  32. 32.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 7 days
  33. 33.If 4 notebooks cost ₹68, how much do 2 notebooks cost? (a) ₹34 (b) ₹66 (c) ₹136 (d) ₹51
  34. 34.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 8 days (d) 2 days
  35. 35.If 6 pens cost ₹48, how much do 4 pens cost? (a) ₹40 (b) ₹46 (c) ₹192 (d) ₹32
  36. 36.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹14 (d) ₹84
  37. 37.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹110 (d) ₹132
  38. 38.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 24 days (d) 14 days
  39. 39.If 9 kites cost ₹180, how much do 3 kites cost? (a) ₹174 (b) ₹60 (c) ₹80 (d) ₹540
  40. 40.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 26 days (d) 17 days

Answer key

  1. ₹80
  2. 8 days
  3. ₹99
  4. ₹44
  5. ₹80
  6. ₹80
  7. ₹168
  8. ₹150
  9. 7 days
  10. ₹60
  11. ₹76
  12. ₹200
  13. ₹296
  14. 9 days
  15. ₹360
  16. 1 day
  17. 24 days
  18. ₹54
  19. ₹63
  20. ₹112
  21. ₹294
  22. ₹150
  23. 10 days
  24. ₹231
  25. 3 days
  26. ₹300
  27. ₹256
  28. ₹132
  29. 18 days
  30. ₹77
  31. ₹55
  32. 4 days
  33. ₹34
  34. 10 days
  35. ₹32
  36. ₹84
  37. ₹110
  38. 24 days
  39. ₹60
  40. 26 days

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