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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 529 · 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.If 8 pens cost ₹56, how much do 12 pens cost? (a) ₹91 (b) ₹60 (c) ₹672 (d) ₹84
  2. 2.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹19 (b) ₹114 (c) ₹38 (d) ₹95
  3. 3.₹196 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹140 (b) ₹56 (c) ₹28 (d) ₹98
  4. 4.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹5 (b) ₹10 (c) ₹30 (d) ₹25
  5. 5.If 8 pens cost ₹192, how much do 12 pens cost? (a) ₹288 (b) ₹196 (c) ₹2304 (d) ₹312
  6. 6.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 2 days
  7. 7.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
  8. 8.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 34 days (c) 15 days (d) 33 days
  9. 9.8 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) 7 days (d) 8 days
  10. 10.If 2 kites cost ₹12, how much do 8 kites cost? (a) ₹48 (b) ₹96 (c) ₹54 (d) ₹18
  11. 11.If 8 mangoes cost ₹24, how much do 5 mangoes cost? (a) ₹18 (b) ₹120 (c) ₹15 (d) ₹21
  12. 12.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹120 (b) ₹135 (c) ₹121 (d) ₹15
  13. 13.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹58 (b) ₹29 (c) ₹59 (d) ₹87
  14. 14.If 6 pens cost ₹72, how much do 8 pens cost? (a) ₹108 (b) ₹96 (c) ₹576 (d) ₹74
  15. 15.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 20 days (d) 6 days
  16. 16.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 31 days (c) 4 days (d) 30 days
  17. 17.If 4 notebooks cost ₹60, how much do 7 notebooks cost? (a) ₹63 (b) ₹420 (c) ₹105 (d) ₹120
  18. 18.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 1 day (d) 11 days
  19. 19.If 2 pens cost ₹12, how much do 4 pens cost? (a) ₹14 (b) ₹48 (c) ₹24 (d) ₹30
  20. 20.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 13 days (d) 14 days
  21. 21.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  22. 22.If 3 kites cost ₹39, how much do 4 kites cost? (a) ₹65 (b) ₹40 (c) ₹52 (d) ₹156
  23. 23.If 4 notebooks cost ₹52, how much do 11 notebooks cost? (a) ₹156 (b) ₹59 (c) ₹572 (d) ₹143
  24. 24.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹50 (b) ₹45 (c) ₹5 (d) ₹25
  25. 25.If 3 kites cost ₹12, how much do 2 kites cost? (a) ₹24 (b) ₹8 (c) ₹11 (d) ₹12
  26. 26.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 22 days (d) 21 days
  27. 27.If 2 kites cost ₹22, how much do 3 kites cost? (a) ₹23 (b) ₹66 (c) ₹33 (d) ₹44
  28. 28.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 30 days (d) 31 days
  29. 29.If 8 mangoes cost ₹136, how much do 9 mangoes cost? (a) ₹170 (b) ₹153 (c) ₹1224 (d) ₹137
  30. 30.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 39 days (d) 17 days
  31. 31.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 10 days (d) 7 days
  32. 32.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 12 days (d) 8 days
  33. 33.If 6 pens cost ₹132, how much do 7 pens cost? (a) ₹924 (b) ₹133 (c) ₹154 (d) ₹176
  34. 34.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 2 days (c) 14 days (d) 33 days
  35. 35.₹270 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹30 (b) ₹135 (c) ₹270 (d) ₹240
  36. 36.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 5 days (d) 8 days
  37. 37.If 7 notebooks cost ₹21, how much do 6 notebooks cost? (a) ₹18 (b) ₹21 (c) ₹126 (d) ₹20
  38. 38.If 3 kites cost ₹12, how much do 4 kites cost? (a) ₹20 (b) ₹16 (c) ₹13 (d) ₹48
  39. 39.If 9 pens cost ₹72, how much do 10 pens cost? (a) ₹720 (b) ₹73 (c) ₹88 (d) ₹80
  40. 40.If 9 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹138 (b) ₹432 (c) ₹48 (d) ₹64

Answer key

  1. ₹84
  2. ₹95
  3. ₹140
  4. ₹25
  5. ₹288
  6. 8 days
  7. 3 days
  8. 33 days
  9. 8 days
  10. ₹48
  11. ₹15
  12. ₹120
  13. ₹58
  14. ₹96
  15. 20 days
  16. 30 days
  17. ₹105
  18. 2 days
  19. ₹24
  20. 14 days
  21. 25 days
  22. ₹52
  23. ₹143
  24. ₹45
  25. ₹8
  26. 21 days
  27. ₹33
  28. 30 days
  29. ₹153
  30. 39 days
  31. 10 days
  32. 12 days
  33. ₹154
  34. 32 days
  35. ₹240
  36. 9 days
  37. ₹18
  38. ₹16
  39. ₹80
  40. ₹48

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