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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 394 · 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 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 14 days (c) 2 days (d) 32 days
  2. 2.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 12 days
  3. 3.If 8 pens cost ₹192, how much do 5 pens cost? (a) ₹144 (b) ₹120 (c) ₹189 (d) ₹960
  4. 4.If 5 notebooks cost ₹90, how much do 3 notebooks cost? (a) ₹54 (b) ₹88 (c) ₹270 (d) ₹72
  5. 5.If 9 pens cost ₹171, how much do 5 pens cost? (a) ₹167 (b) ₹855 (c) ₹95 (d) ₹114
  6. 6.If 3 mangoes cost ₹54, how much do 2 mangoes cost? (a) ₹53 (b) ₹108 (c) ₹54 (d) ₹36
  7. 7.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
  8. 8.If 6 pens cost ₹30, how much do 7 pens cost? (a) ₹31 (b) ₹210 (c) ₹40 (d) ₹35
  9. 9.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹17 (b) ₹34 (c) ₹119 (d) ₹136
  10. 10.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 45 days (c) 5 days (d) 19 days
  11. 11.₹330 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹297 (b) ₹33 (c) ₹165 (d) ₹330
  12. 12.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 20 days (d) 5 days
  13. 13.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 19 days (d) 6 days
  14. 14.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹217 (b) ₹248 (c) ₹124 (d) ₹31
  15. 15.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 21 days (d) 22 days
  16. 16.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 15 days (d) 11 days
  17. 17.If 3 notebooks cost ₹42, how much do 8 notebooks cost? (a) ₹336 (b) ₹47 (c) ₹112 (d) ₹126
  18. 18.If 4 pens cost ₹52, how much do 8 pens cost? (a) ₹117 (b) ₹104 (c) ₹416 (d) ₹56
  19. 19.If 7 pens cost ₹70, how much do 4 pens cost? (a) ₹280 (b) ₹67 (c) ₹40 (d) ₹50
  20. 20.₹161 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹138 (b) ₹115 (c) ₹46 (d) ₹23
  21. 21.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹320 (b) ₹120 (c) ₹40 (d) ₹220
  22. 22.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹83 (b) ₹123 (c) ₹41 (d) ₹82
  23. 23.If 5 kites cost ₹35, how much do 4 kites cost? (a) ₹140 (b) ₹34 (c) ₹28 (d) ₹35
  24. 24.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹136 (b) ₹51 (c) ₹153 (d) ₹17
  25. 25.If 7 mangoes cost ₹21, how much do 8 mangoes cost? (a) ₹27 (b) ₹168 (c) ₹24 (d) ₹22
  26. 26.₹238 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹119 (b) ₹170 (c) ₹68 (d) ₹34
  27. 27.If 5 pens cost ₹20, how much do 4 pens cost? (a) ₹19 (b) ₹16 (c) ₹20 (d) ₹80
  28. 28.If 3 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹72 (c) ₹80 (d) ₹30
  29. 29.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 14 days (d) 3 days
  30. 30.If 9 mangoes cost ₹126, how much do 3 mangoes cost? (a) ₹120 (b) ₹378 (c) ₹42 (d) ₹56
  31. 31.If 8 kites cost ₹104, how much do 3 kites cost? (a) ₹52 (b) ₹312 (c) ₹39 (d) ₹99
  32. 32.If 4 pens cost ₹84, how much do 3 pens cost? (a) ₹83 (b) ₹63 (c) ₹252 (d) ₹84
  33. 33.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 28 days (d) 19 days
  34. 34.If 5 mangoes cost ₹25, how much do 11 mangoes cost? (a) ₹275 (b) ₹31 (c) ₹55 (d) ₹60
  35. 35.If 4 pens cost ₹20, how much do 12 pens cost? (a) ₹28 (b) ₹60 (c) ₹65 (d) ₹240
  36. 36.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 6 days
  37. 37.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹80 (c) ₹128 (d) ₹16
  38. 38.If 7 kites cost ₹35, how much do 8 kites cost? (a) ₹280 (b) ₹40 (c) ₹45 (d) ₹36
  39. 39.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 11 days (c) 15 days (d) 26 days
  40. 40.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 52 days (c) 19 days (d) 7 days

Answer key

  1. 32 days
  2. 3 days
  3. ₹120
  4. ₹54
  5. ₹95
  6. ₹36
  7. 3 days
  8. ₹35
  9. ₹119
  10. 45 days
  11. ₹297
  12. 5 days
  13. 5 days
  14. ₹217
  15. 21 days
  16. 14 days
  17. ₹112
  18. ₹104
  19. ₹40
  20. ₹115
  21. ₹320
  22. ₹82
  23. ₹28
  24. ₹136
  25. ₹24
  26. ₹170
  27. ₹16
  28. ₹72
  29. 4 days
  30. ₹42
  31. ₹39
  32. ₹63
  33. 27 days
  34. ₹55
  35. ₹60
  36. 3 days
  37. ₹128
  38. ₹40
  39. 26 days
  40. 52 days

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