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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 841 · 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. 1.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 9 days (d) 10 days
  2. 2.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 42 days (d) 43 days
  3. 3.₹143 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹39 (b) ₹117 (c) ₹13 (d) ₹104
  4. 4.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹23 (c) ₹47 (d) ₹46
  5. 5.If 8 pens cost ₹136, how much do 2 pens cost? (a) ₹272 (b) ₹130 (c) ₹51 (d) ₹34
  6. 6.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 9 days (d) 8 days
  7. 7.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹315 (d) ₹175
  8. 8.If 8 pens cost ₹72, how much do 6 pens cost? (a) ₹54 (b) ₹70 (c) ₹63 (d) ₹432
  9. 9.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 13 days (d) 19 days
  10. 10.If 5 pens cost ₹105, how much do 6 pens cost? (a) ₹106 (b) ₹147 (c) ₹630 (d) ₹126
  11. 11.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹46 (b) ₹322 (c) ₹414 (d) ₹230
  12. 12.If 5 pens cost ₹20, how much do 8 pens cost? (a) ₹160 (b) ₹23 (c) ₹36 (d) ₹32
  13. 13.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 10 days (d) 9 days
  14. 14.If 8 pens cost ₹40, how much do 3 pens cost? (a) ₹20 (b) ₹15 (c) ₹120 (d) ₹35
  15. 15.₹220 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹220 (b) ₹176 (c) ₹110 (d) ₹44
  16. 16.If 6 mangoes cost ₹150, how much do 12 mangoes cost? (a) ₹156 (b) ₹1800 (c) ₹300 (d) ₹325
  17. 17.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹45 (b) ₹60 (c) ₹30 (d) ₹15
  18. 18.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹18 (b) ₹48 (c) ₹33 (d) ₹6
  19. 19.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 45 days (d) 5 days
  20. 20.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 4 days (d) 3 days
  21. 21.8 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
  22. 22.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹175 (d) ₹210
  23. 23.If 9 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹648 (b) ₹57 (c) ₹78 (d) ₹72
  24. 24.If 4 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹99 (b) ₹360 (c) ₹90 (d) ₹42
  25. 25.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹84 (b) ₹378 (c) ₹42 (d) ₹231
  26. 26.If 5 notebooks cost ₹30, how much do 9 notebooks cost? (a) ₹34 (b) ₹60 (c) ₹270 (d) ₹54
  27. 27.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹20 (c) ₹5 (d) ₹40
  28. 28.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
  29. 29.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 56 days (c) 8 days (d) 20 days
  30. 30.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 9 days (d) 17 days
  31. 31.If 5 pens cost ₹65, how much do 6 pens cost? (a) ₹78 (b) ₹66 (c) ₹91 (d) ₹390
  32. 32.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 10 days (d) 4 days
  33. 33.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 8 days
  34. 34.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹49 (d) ₹7
  35. 35.If 9 pens cost ₹108, how much do 11 pens cost? (a) ₹1188 (b) ₹110 (c) ₹144 (d) ₹132
  36. 36.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 13 days (d) 5 days
  37. 37.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 4 days
  38. 38.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 11 days (d) 10 days
  39. 39.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 4 days (c) 9 days (d) 19 days
  40. 40.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹45 (d) ₹72

Answer key

  1. 9 days
  2. 42 days
  3. ₹104
  4. ₹46
  5. ₹34
  6. 8 days
  7. ₹315
  8. ₹54
  9. 18 days
  10. ₹126
  11. ₹414
  12. ₹32
  13. 9 days
  14. ₹15
  15. ₹176
  16. ₹300
  17. ₹45
  18. ₹48
  19. 5 days
  20. 9 days
  21. 4 days
  22. ₹245
  23. ₹72
  24. ₹90
  25. ₹378
  26. ₹54
  27. ₹35
  28. 9 days
  29. 56 days
  30. 26 days
  31. ₹78
  32. 4 days
  33. 12 days
  34. ₹49
  35. ₹132
  36. 6 days
  37. 6 days
  38. 10 days
  39. 49 days
  40. ₹72

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