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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 953 · 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. 1.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 8 days (d) 11 days
  2. 2.If 9 notebooks cost ₹153, how much do 7 notebooks cost? (a) ₹1071 (b) ₹119 (c) ₹151 (d) ₹136
  3. 3.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹44 (b) ₹220 (c) ₹264 (d) ₹308
  4. 4.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹70 (b) ₹210 (c) ₹35 (d) ₹175
  5. 5.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹128 (b) ₹32 (c) ₹96 (d) ₹160
  6. 6.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹75 (c) ₹15 (d) ₹60
  7. 7.If 3 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹67 (b) ₹110 (c) ₹264 (d) ₹88
  8. 8.If 4 notebooks cost ₹92, how much do 5 notebooks cost? (a) ₹138 (b) ₹115 (c) ₹93 (d) ₹460
  9. 9.If 6 kites cost ₹54, how much do 3 kites cost? (a) ₹162 (b) ₹36 (c) ₹27 (d) ₹51
  10. 10.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 17 days (d) 11 days
  11. 11.If 6 mangoes cost ₹150, how much do 10 mangoes cost? (a) ₹275 (b) ₹154 (c) ₹1500 (d) ₹250
  12. 12.If 4 kites cost ₹100, how much do 5 kites cost? (a) ₹500 (b) ₹150 (c) ₹125 (d) ₹101
  13. 13.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹245 (d) ₹196
  14. 14.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 8 days (d) 10 days
  15. 15.₹120 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹120 (b) ₹60 (c) ₹105 (d) ₹15
  16. 16.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹164 (b) ₹123 (c) ₹41 (d) ₹205
  17. 17.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 16 days (d) 10 days
  18. 18.If 6 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹26 (b) ₹36 (c) ₹32 (d) ₹192
  19. 19.If 2 pens cost ₹16, how much do 3 pens cost? (a) ₹48 (b) ₹32 (c) ₹24 (d) ₹17
  20. 20.If 6 pens cost ₹126, how much do 8 pens cost? (a) ₹1008 (b) ₹189 (c) ₹168 (d) ₹128
  21. 21.If 3 pens cost ₹12, how much do 2 pens cost? (a) ₹11 (b) ₹8 (c) ₹24 (d) ₹12
  22. 22.If 3 mangoes cost ₹63, how much do 2 mangoes cost? (a) ₹63 (b) ₹126 (c) ₹42 (d) ₹62
  23. 23.₹77 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹63 (b) ₹70 (c) ₹7 (d) ₹14
  24. 24.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 1 day
  25. 25.₹56 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹28 (d) ₹40
  26. 26.If 6 notebooks cost ₹54, how much do 8 notebooks cost? (a) ₹432 (b) ₹81 (c) ₹56 (d) ₹72
  27. 27.₹260 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹78 (b) ₹26 (c) ₹182 (d) ₹130
  28. 28.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹144 (b) ₹96 (c) ₹192 (d) ₹48
  29. 29.If 4 notebooks cost ₹76, how much do 5 notebooks cost? (a) ₹77 (b) ₹114 (c) ₹380 (d) ₹95
  30. 30.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 2 days (d) 3 days
  31. 31.If 4 mangoes cost ₹24, how much do 2 mangoes cost? (a) ₹22 (b) ₹48 (c) ₹18 (d) ₹12
  32. 32.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
  33. 33.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹160 (b) ₹48 (c) ₹40 (d) ₹33
  34. 34.If 7 notebooks cost ₹49, how much do 9 notebooks cost? (a) ₹441 (b) ₹51 (c) ₹70 (d) ₹63
  35. 35.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹36 (d) ₹72
  36. 36.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹40 (b) ₹70 (c) ₹100 (d) ₹20
  37. 37.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 25 days (c) 14 days (d) 24 days
  38. 38.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹18 (c) ₹48 (d) ₹6
  39. 39.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 36 days (d) 11 days
  40. 40.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹216 (c) ₹243 (d) ₹27

Answer key

  1. 8 days
  2. ₹119
  3. ₹308
  4. ₹175
  5. ₹160
  6. ₹60
  7. ₹88
  8. ₹115
  9. ₹27
  10. 12 days
  11. ₹250
  12. ₹125
  13. ₹196
  14. 9 days
  15. ₹105
  16. ₹205
  17. 16 days
  18. ₹32
  19. ₹24
  20. ₹168
  21. ₹8
  22. ₹42
  23. ₹63
  24. 6 days
  25. ₹40
  26. ₹72
  27. ₹182
  28. ₹144
  29. ₹95
  30. 3 days
  31. ₹12
  32. 3 days
  33. ₹40
  34. ₹63
  35. ₹108
  36. ₹100
  37. 24 days
  38. ₹48
  39. 35 days
  40. ₹216

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