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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 606 · 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.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹124 (b) ₹248 (c) ₹31 (d) ₹217
  2. 2.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹23 (b) ₹69 (c) ₹46 (d) ₹92
  3. 3.8 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 24 days (d) 16 days
  4. 4.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹47 (b) ₹377 (c) ₹376 (d) ₹423
  5. 5.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 10 days (d) 11 days
  6. 6.If 2 mangoes cost ₹14, how much do 6 mangoes cost? (a) ₹84 (b) ₹42 (c) ₹49 (d) ₹18
  7. 7.If 9 mangoes cost ₹216, how much do 10 mangoes cost? (a) ₹264 (b) ₹240 (c) ₹217 (d) ₹2160
  8. 8.If 8 notebooks cost ₹136, how much do 5 notebooks cost? (a) ₹133 (b) ₹85 (c) ₹102 (d) ₹680
  9. 9.If 8 notebooks cost ₹184, how much do 12 notebooks cost? (a) ₹2208 (b) ₹299 (c) ₹188 (d) ₹276
  10. 10.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 9 days (d) 4 days
  11. 11.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹8 (b) ₹48 (c) ₹56 (d) ₹40
  12. 12.If 5 kites cost ₹90, how much do 8 kites cost? (a) ₹162 (b) ₹93 (c) ₹720 (d) ₹144
  13. 13.If 6 pens cost ₹90, how much do 4 pens cost? (a) ₹75 (b) ₹360 (c) ₹88 (d) ₹60
  14. 14.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹21 (b) ₹12 (c) ₹30 (d) ₹6
  15. 15.If 4 kites cost ₹32, how much do 5 kites cost? (a) ₹33 (b) ₹48 (c) ₹40 (d) ₹160
  16. 16.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
  17. 17.₹315 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹225 (c) ₹270 (d) ₹45
  18. 18.If 6 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹39 (b) ₹324 (c) ₹60 (d) ₹54
  19. 19.If 4 pens cost ₹64, how much do 5 pens cost? (a) ₹96 (b) ₹65 (c) ₹320 (d) ₹80
  20. 20.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 2 days (d) 6 days
  21. 21.If 6 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹40 (b) ₹240 (c) ₹47 (d) ₹48
  22. 22.If 3 kites cost ₹30, how much do 5 kites cost? (a) ₹60 (b) ₹50 (c) ₹150 (d) ₹32
  23. 23.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
  24. 24.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹135 (b) ₹15 (c) ₹30 (d) ₹150
  25. 25.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 16 days (c) 8 days (d) 28 days
  26. 26.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹91 (b) ₹110 (c) ₹900 (d) ₹100
  27. 27.If 8 mangoes cost ₹192, how much do 7 mangoes cost? (a) ₹191 (b) ₹192 (c) ₹1344 (d) ₹168
  28. 28.If 9 mangoes cost ₹63, how much do 10 mangoes cost? (a) ₹630 (b) ₹64 (c) ₹77 (d) ₹70
  29. 29.If 6 mangoes cost ₹114, how much do 5 mangoes cost? (a) ₹113 (b) ₹114 (c) ₹95 (d) ₹570
  30. 30.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹20 (c) ₹30 (d) ₹40
  31. 31.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 5 days (d) 4 days
  32. 32.If 5 pens cost ₹105, how much do 6 pens cost? (a) ₹147 (b) ₹630 (c) ₹126 (d) ₹106
  33. 33.If 2 notebooks cost ₹10, how much do 4 notebooks cost? (a) ₹25 (b) ₹12 (c) ₹20 (d) ₹40
  34. 34.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 6 days (d) 36 days
  35. 35.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 31 days (d) 30 days
  36. 36.If 6 kites cost ₹48, how much do 9 kites cost? (a) ₹432 (b) ₹80 (c) ₹51 (d) ₹72
  37. 37.If 6 pens cost ₹138, how much do 10 pens cost? (a) ₹142 (b) ₹1380 (c) ₹253 (d) ₹230
  38. 38.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹60 (b) ₹160 (c) ₹110 (d) ₹20
  39. 39.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹48 (b) ₹64 (c) ₹80 (d) ₹16
  40. 40.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 20 days (d) 4 days

Answer key

  1. ₹217
  2. ₹69
  3. 24 days
  4. ₹376
  5. 10 days
  6. ₹42
  7. ₹240
  8. ₹85
  9. ₹276
  10. 49 days
  11. ₹56
  12. ₹144
  13. ₹60
  14. ₹30
  15. ₹40
  16. 5 days
  17. ₹225
  18. ₹54
  19. ₹80
  20. 8 days
  21. ₹40
  22. ₹50
  23. 9 days
  24. ₹135
  25. 28 days
  26. ₹100
  27. ₹168
  28. ₹70
  29. ₹95
  30. ₹40
  31. 5 days
  32. ₹126
  33. ₹20
  34. 36 days
  35. 30 days
  36. ₹72
  37. ₹230
  38. ₹160
  39. ₹80
  40. 5 days

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