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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 207 · 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 5 notebooks cost ₹20, how much do 4 notebooks cost? (a) ₹20 (b) ₹80 (c) ₹19 (d) ₹16
  2. 2.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 40 days (d) 39 days
  3. 3.If 8 mangoes cost ₹160, how much do 9 mangoes cost? (a) ₹1440 (b) ₹200 (c) ₹180 (d) ₹161
  4. 4.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 7 days (d) 8 days
  5. 5.If 9 notebooks cost ₹189, how much do 2 notebooks cost? (a) ₹182 (b) ₹63 (c) ₹378 (d) ₹42
  6. 6.₹360 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹40 (b) ₹180 (c) ₹280 (d) ₹80
  7. 7.If 7 mangoes cost ₹126, how much do 5 mangoes cost? (a) ₹124 (b) ₹630 (c) ₹90 (d) ₹108
  8. 8.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹81 (c) ₹54 (d) ₹55
  9. 9.₹414 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹414 (b) ₹46 (c) ₹368 (d) ₹207
  10. 10.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹75 (b) ₹150 (c) ₹50 (d) ₹100
  11. 11.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹120 (d) ₹280
  12. 12.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
  13. 13.If 9 notebooks cost ₹225, how much do 10 notebooks cost? (a) ₹226 (b) ₹275 (c) ₹2250 (d) ₹250
  14. 14.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹85 (b) ₹153 (c) ₹17 (d) ₹119
  15. 15.If 8 pens cost ₹120, how much do 3 pens cost? (a) ₹115 (b) ₹45 (c) ₹60 (d) ₹360
  16. 16.If 9 notebooks cost ₹126, how much do 5 notebooks cost? (a) ₹84 (b) ₹122 (c) ₹630 (d) ₹70
  17. 17.If 5 notebooks cost ₹55, how much do 8 notebooks cost? (a) ₹58 (b) ₹99 (c) ₹88 (d) ₹440
  18. 18.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 18 days (d) 12 days
  19. 19.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 1 day (d) 10 days
  20. 20.If 9 mangoes cost ₹180, how much do 4 mangoes cost? (a) ₹80 (b) ₹720 (c) ₹175 (d) ₹100
  21. 21.₹559 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹215 (b) ₹387 (c) ₹43 (d) ₹344
  22. 22.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹15 (b) ₹105 (c) ₹60 (d) ₹120
  23. 23.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹230 (b) ₹161 (c) ₹46 (d) ₹92
  24. 24.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 16 days (d) 9 days
  25. 25.If 2 kites cost ₹32, how much do 11 kites cost? (a) ₹41 (b) ₹352 (c) ₹176 (d) ₹192
  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) 21 days (d) 22 days
  27. 27.If 3 mangoes cost ₹21, how much do 2 mangoes cost? (a) ₹14 (b) ₹42 (c) ₹20 (d) ₹21
  28. 28.If 9 mangoes cost ₹135, how much do 6 mangoes cost? (a) ₹810 (b) ₹105 (c) ₹90 (d) ₹132
  29. 29.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 4 days (d) 3 days
  30. 30.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 11 days (d) 6 days
  31. 31.If 8 pens cost ₹24, how much do 9 pens cost? (a) ₹30 (b) ₹216 (c) ₹27 (d) ₹25
  32. 32.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹220 (b) ₹264 (c) ₹308 (d) ₹44
  33. 33.₹336 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹126 (b) ₹42 (c) ₹210 (d) ₹168
  34. 34.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 4 days
  35. 35.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 16 days (d) 24 days
  36. 36.If 4 notebooks cost ₹68, how much do 7 notebooks cost? (a) ₹71 (b) ₹136 (c) ₹119 (d) ₹476
  37. 37.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹21 (b) ₹14 (c) ₹15 (d) ₹7
  38. 38.If 8 pens cost ₹192, how much do 10 pens cost? (a) ₹240 (b) ₹1920 (c) ₹264 (d) ₹194
  39. 39.₹70 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹45 (d) ₹25
  40. 40.If 5 kites cost ₹110, how much do 8 kites cost? (a) ₹198 (b) ₹176 (c) ₹113 (d) ₹880

Answer key

  1. ₹16
  2. 39 days
  3. ₹180
  4. 7 days
  5. ₹42
  6. ₹280
  7. ₹90
  8. ₹54
  9. ₹368
  10. ₹100
  11. ₹280
  12. 6 days
  13. ₹250
  14. ₹153
  15. ₹45
  16. ₹70
  17. ₹88
  18. 18 days
  19. 10 days
  20. ₹80
  21. ₹344
  22. ₹105
  23. ₹230
  24. 15 days
  25. ₹176
  26. 21 days
  27. ₹14
  28. ₹90
  29. 4 days
  30. 7 days
  31. ₹27
  32. ₹308
  33. ₹210
  34. 4 days
  35. 6 days
  36. ₹119
  37. ₹14
  38. ₹240
  39. ₹45
  40. ₹176

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