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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 960 · 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 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 40 days (d) 19 days
  2. 2.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 4 days (d) 16 days
  3. 3.₹84 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹12 (b) ₹42 (c) ₹24 (d) ₹60
  4. 4.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹196 (d) ₹147
  5. 5.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
  6. 6.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹91
  7. 7.If 4 mangoes cost ₹12, how much do 2 mangoes cost? (a) ₹24 (b) ₹10 (c) ₹9 (d) ₹6
  8. 8.If 8 pens cost ₹96, how much do 7 pens cost? (a) ₹672 (b) ₹95 (c) ₹84 (d) ₹96
  9. 9.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
  10. 10.8 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
  11. 11.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 9 days (d) 7 days
  12. 12.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 18 days
  13. 13.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 23 days (d) 22 days
  14. 14.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 10 days (d) 11 days
  15. 15.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 13 days (d) 5 days
  16. 16.If 2 pens cost ₹20, how much do 8 pens cost? (a) ₹26 (b) ₹80 (c) ₹160 (d) ₹90
  17. 17.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 25 days (c) 12 days (d) 24 days
  18. 18.If 4 notebooks cost ₹72, how much do 8 notebooks cost? (a) ₹76 (b) ₹144 (c) ₹576 (d) ₹162
  19. 19.If 4 pens cost ₹64, how much do 2 pens cost? (a) ₹48 (b) ₹128 (c) ₹32 (d) ₹62
  20. 20.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 10 days
  21. 21.If 2 pens cost ₹16, how much do 9 pens cost? (a) ₹144 (b) ₹80 (c) ₹23 (d) ₹72
  22. 22.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹150 (c) ₹125 (d) ₹175
  23. 23.₹260 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹130 (b) ₹80 (c) ₹20 (d) ₹180
  24. 24.₹195 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹157 (d) ₹156
  25. 25.If 7 notebooks cost ₹133, how much do 2 notebooks cost? (a) ₹38 (b) ₹128 (c) ₹57 (d) ₹266
  26. 26.If 7 mangoes cost ₹140, how much do 8 mangoes cost? (a) ₹180 (b) ₹1120 (c) ₹141 (d) ₹160
  27. 27.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹33 (d) ₹22
  28. 28.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 7 days (c) 28 days (d) 16 days
  29. 29.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 25 days (d) 17 days
  30. 30.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹29 (b) ₹117 (c) ₹116 (d) ₹145
  31. 31.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹84 (b) ₹120 (c) ₹24 (d) ₹48
  32. 32.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 2 days (c) 6 days (d) 7 days
  33. 33.If 7 pens cost ₹49, how much do 12 pens cost? (a) ₹91 (b) ₹588 (c) ₹84 (d) ₹54
  34. 34.If 4 kites cost ₹88, how much do 2 kites cost? (a) ₹176 (b) ₹44 (c) ₹66 (d) ₹86
  35. 35.If 2 mangoes cost ₹50, how much do 4 mangoes cost? (a) ₹200 (b) ₹100 (c) ₹125 (d) ₹52
  36. 36.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 6 days
  37. 37.₹234 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹90 (c) ₹18 (d) ₹144
  38. 38.If 2 mangoes cost ₹40, how much do 11 mangoes cost? (a) ₹49 (b) ₹240 (c) ₹440 (d) ₹220
  39. 39.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹23 (b) ₹230 (c) ₹92 (d) ₹207
  40. 40.If 7 mangoes cost ₹56, how much do 2 mangoes cost? (a) ₹51 (b) ₹24 (c) ₹112 (d) ₹16

Answer key

  1. 39 days
  2. 16 days
  3. ₹60
  4. ₹147
  5. 3 days
  6. ₹91
  7. ₹6
  8. ₹84
  9. 27 days
  10. 52 days
  11. 8 days
  12. 6 days
  13. 22 days
  14. 10 days
  15. 27 days
  16. ₹80
  17. 24 days
  18. ₹144
  19. ₹32
  20. 9 days
  21. ₹72
  22. ₹150
  23. ₹180
  24. ₹156
  25. ₹38
  26. ₹160
  27. ₹33
  28. 28 days
  29. 9 days
  30. ₹116
  31. ₹120
  32. 6 days
  33. ₹84
  34. ₹44
  35. ₹100
  36. 5 days
  37. ₹144
  38. ₹220
  39. ₹207
  40. ₹16

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