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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 691 · 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 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 9 days (d) 10 days
  2. 2.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 9 days (d) 15 days
  3. 3.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 17 days (d) 11 days
  4. 4.If 7 kites cost ₹161, how much do 5 kites cost? (a) ₹115 (b) ₹159 (c) ₹138 (d) ₹805
  5. 5.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹145 (b) ₹116 (c) ₹29 (d) ₹117
  6. 6.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 7 days
  7. 7.If 2 pens cost ₹14, how much do 4 pens cost? (a) ₹56 (b) ₹16 (c) ₹35 (d) ₹28
  8. 8.If 4 mangoes cost ₹68, how much do 2 mangoes cost? (a) ₹136 (b) ₹51 (c) ₹66 (d) ₹34
  9. 9.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 23 days (b) 45 days (c) 5 days (d) 7 days
  10. 10.If 9 pens cost ₹90, how much do 6 pens cost? (a) ₹540 (b) ₹87 (c) ₹60 (d) ₹70
  11. 11.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹60 (b) ₹15 (c) ₹18 (d) ₹13
  12. 12.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 15 days (d) 14 days
  13. 13.If 7 pens cost ₹161, how much do 8 pens cost? (a) ₹184 (b) ₹1288 (c) ₹162 (d) ₹207
  14. 14.If 7 pens cost ₹28, how much do 12 pens cost? (a) ₹48 (b) ₹52 (c) ₹33 (d) ₹336
  15. 15.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 28 days (d) 7 days
  16. 16.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
  17. 17.If 8 pens cost ₹72, how much do 2 pens cost? (a) ₹27 (b) ₹18 (c) ₹144 (d) ₹66
  18. 18.If 8 kites cost ₹48, how much do 9 kites cost? (a) ₹432 (b) ₹60 (c) ₹49 (d) ₹54
  19. 19.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 12 days (d) 4 days
  20. 20.If 4 notebooks cost ₹44, how much do 9 notebooks cost? (a) ₹49 (b) ₹110 (c) ₹396 (d) ₹99
  21. 21.If 7 mangoes cost ₹77, how much do 3 mangoes cost? (a) ₹231 (b) ₹44 (c) ₹73 (d) ₹33
  22. 22.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 13 days (d) 12 days
  23. 23.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹21 (b) ₹189 (c) ₹147 (d) ₹105
  24. 24.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 32 days (c) 2 days (d) 14 days
  25. 25.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 14 days (d) 15 days
  26. 26.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 2 days (d) 3 days
  27. 27.If 7 notebooks cost ₹28, how much do 8 notebooks cost? (a) ₹36 (b) ₹224 (c) ₹32 (d) ₹29
  28. 28.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹35 (b) ₹28 (c) ₹14 (d) ₹42
  29. 29.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 8 days
  30. 30.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
  31. 31.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹144 (b) ₹264 (c) ₹384 (d) ₹48
  32. 32.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 10 days (c) 2 days (d) 18 days
  33. 33.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹208 (b) ₹104 (c) ₹26 (d) ₹182
  34. 34.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 20 days (d) 6 days
  35. 35.If 7 mangoes cost ₹28, how much do 9 mangoes cost? (a) ₹40 (b) ₹30 (c) ₹36 (d) ₹252
  36. 36.If 5 mangoes cost ₹60, how much do 8 mangoes cost? (a) ₹96 (b) ₹108 (c) ₹63 (d) ₹480
  37. 37.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹80 (d) ₹70
  38. 38.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 3 days (d) 4 days
  39. 39.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹123 (b) ₹82 (c) ₹83 (d) ₹41
  40. 40.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 12 days (d) 8 days

Answer key

  1. 9 days
  2. 14 days
  3. 8 days
  4. ₹115
  5. ₹116
  6. 5 days
  7. ₹28
  8. ₹34
  9. 5 days
  10. ₹60
  11. ₹15
  12. 14 days
  13. ₹184
  14. ₹48
  15. 7 days
  16. 49 days
  17. ₹18
  18. ₹54
  19. 16 days
  20. ₹99
  21. ₹33
  22. 12 days
  23. ₹189
  24. 32 days
  25. 14 days
  26. 3 days
  27. ₹32
  28. ₹42
  29. 6 days
  30. 22 days
  31. ₹384
  32. 18 days
  33. ₹182
  34. 5 days
  35. ₹36
  36. ₹96
  37. ₹70
  38. 4 days
  39. ₹82
  40. 6 days

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