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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 264 · 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 2 kites cost ₹18, how much do 8 kites cost? (a) ₹24 (b) ₹72 (c) ₹144 (d) ₹81
  2. 2.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹5 (c) ₹35 (d) ₹20
  3. 3.5 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) 6 days (d) 20 days
  4. 4.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 13 days
  5. 5.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 7 days (d) 23 days
  6. 6.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 15 days (c) 36 days (d) 1 day
  7. 7.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹261 (b) ₹145 (c) ₹29 (d) ₹290
  8. 8.If 2 mangoes cost ₹50, how much do 4 mangoes cost? (a) ₹200 (b) ₹52 (c) ₹125 (d) ₹100
  9. 9.If 4 kites cost ₹36, how much do 5 kites cost? (a) ₹37 (b) ₹180 (c) ₹45 (d) ₹54
  10. 10.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 13 days (d) 5 days
  11. 11.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 4 days (d) 9 days
  12. 12.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 1 day (d) 7 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) 22 days (c) 9 days (d) 23 days
  14. 14.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
  15. 15.If 7 kites cost ₹91, how much do 4 kites cost? (a) ₹65 (b) ₹52 (c) ₹364 (d) ₹88
  16. 16.If 9 mangoes cost ₹81, how much do 12 mangoes cost? (a) ₹972 (b) ₹117 (c) ₹84 (d) ₹108
  17. 17.If 4 mangoes cost ₹92, how much do 12 mangoes cost? (a) ₹299 (b) ₹1104 (c) ₹276 (d) ₹100
  18. 18.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 5 days
  19. 19.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹175 (c) ₹35 (d) ₹140
  20. 20.If 5 kites cost ₹90, how much do 6 kites cost? (a) ₹540 (b) ₹108 (c) ₹126 (d) ₹91
  21. 21.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹108 (c) ₹162 (d) ₹27
  22. 22.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹26 (b) ₹91 (c) ₹104 (d) ₹13
  23. 23.If 6 kites cost ₹66, how much do 5 kites cost? (a) ₹65 (b) ₹55 (c) ₹330 (d) ₹66
  24. 24.If 6 notebooks cost ₹108, how much do 11 notebooks cost? (a) ₹216 (b) ₹1188 (c) ₹113 (d) ₹198
  25. 25.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹80 (c) ₹16 (d) ₹64
  26. 26.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 4 days (d) 3 days
  27. 27.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 4 days
  28. 28.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 17 days
  29. 29.If 4 notebooks cost ₹56, how much do 3 notebooks cost? (a) ₹168 (b) ₹56 (c) ₹55 (d) ₹42
  30. 30.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
  31. 31.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹68 (b) ₹34 (c) ₹17 (d) ₹51
  32. 32.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹200 (c) ₹40 (d) ₹240
  33. 33.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 17 days (d) 15 days
  34. 34.₹252 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹126 (c) ₹36 (d) ₹144
  35. 35.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹60 (b) ₹108 (c) ₹19 (d) ₹54
  36. 36.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 9 days (d) 4 days
  37. 37.If 8 kites cost ₹144, how much do 5 kites cost? (a) ₹90 (b) ₹720 (c) ₹108 (d) ₹141
  38. 38.If 4 pens cost ₹76, how much do 8 pens cost? (a) ₹152 (b) ₹608 (c) ₹80 (d) ₹171
  39. 39.If 8 pens cost ₹152, how much do 7 pens cost? (a) ₹151 (b) ₹1064 (c) ₹152 (d) ₹133
  40. 40.If 6 kites cost ₹90, how much do 4 kites cost? (a) ₹60 (b) ₹88 (c) ₹360 (d) ₹75

Answer key

  1. ₹72
  2. ₹35
  3. 5 days
  4. 9 days
  5. 22 days
  6. 36 days
  7. ₹261
  8. ₹100
  9. ₹45
  10. 20 days
  11. 49 days
  12. 10 days
  13. 22 days
  14. 3 days
  15. ₹52
  16. ₹108
  17. ₹276
  18. 4 days
  19. ₹140
  20. ₹108
  21. ₹135
  22. ₹91
  23. ₹55
  24. ₹198
  25. ₹64
  26. 3 days
  27. 4 days
  28. 3 days
  29. ₹42
  30. 25 days
  31. ₹51
  32. ₹240
  33. 16 days
  34. ₹144
  35. ₹54
  36. 9 days
  37. ₹90
  38. ₹152
  39. ₹133
  40. ₹60

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