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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 834 · 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 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹36 (b) ₹240 (c) ₹45 (d) ₹30
  2. 2.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹45 (b) ₹90 (c) ₹30 (d) ₹60
  3. 3.If 6 pens cost ₹114, how much do 5 pens cost? (a) ₹114 (b) ₹113 (c) ₹95 (d) ₹570
  4. 4.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 7 days (c) 10 days (d) 6 days
  5. 5.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹26 (d) ₹52
  6. 6.If 2 kites cost ₹34, how much do 9 kites cost? (a) ₹306 (b) ₹41 (c) ₹170 (d) ₹153
  7. 7.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹135 (d) ₹91
  8. 8.If 4 pens cost ₹80, how much do 11 pens cost? (a) ₹220 (b) ₹880 (c) ₹240 (d) ₹87
  9. 9.If 4 kites cost ₹52, how much do 3 kites cost? (a) ₹39 (b) ₹52 (c) ₹51 (d) ₹156
  10. 10.If 6 kites cost ₹48, how much do 2 kites cost? (a) ₹44 (b) ₹24 (c) ₹96 (d) ₹16
  11. 11.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 1 day (d) 17 days
  12. 12.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 18 days (d) 11 days
  13. 13.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹8 (b) ₹48 (c) ₹40 (d) ₹44
  14. 14.If 5 notebooks cost ₹15, how much do 6 notebooks cost? (a) ₹90 (b) ₹16 (c) ₹21 (d) ₹18
  15. 15.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 4 days (d) 3 days
  16. 16.₹228 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹190 (b) ₹228 (c) ₹38 (d) ₹114
  17. 17.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 12 days (c) 13 days (d) 6 days
  18. 18.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹58 (b) ₹29 (c) ₹174 (d) ₹145
  19. 19.₹135 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹54 (b) ₹108 (c) ₹27 (d) ₹81
  20. 20.₹80 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹56 (b) ₹24 (c) ₹40 (d) ₹8
  21. 21.₹60 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹40 (d) ₹60
  22. 22.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹72 (b) ₹48 (c) ₹96 (d) ₹24
  23. 23.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 1 day (c) 13 days (d) 29 days
  24. 24.If 8 pens cost ₹40, how much do 7 pens cost? (a) ₹39 (b) ₹35 (c) ₹40 (d) ₹280
  25. 25.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹90 (d) ₹126
  26. 26.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹190 (b) ₹304 (c) ₹38 (d) ₹247
  27. 27.If 5 kites cost ₹120, how much do 10 kites cost? (a) ₹240 (b) ₹125 (c) ₹1200 (d) ₹264
  28. 28.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 17 days
  29. 29.If 2 pens cost ₹20, how much do 10 pens cost? (a) ₹200 (b) ₹100 (c) ₹110 (d) ₹28
  30. 30.If 6 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹66 (b) ₹60 (c) ₹40 (d) ₹360
  31. 31.If 4 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹75 (b) ₹300 (c) ₹90 (d) ₹61
  32. 32.If 4 pens cost ₹88, how much do 3 pens cost? (a) ₹87 (b) ₹88 (c) ₹264 (d) ₹66
  33. 33.If 2 mangoes cost ₹28, how much do 12 mangoes cost? (a) ₹182 (b) ₹38 (c) ₹336 (d) ₹168
  34. 34.If 4 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹21 (c) ₹27 (d) ₹28
  35. 35.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹90 (b) ₹55 (c) ₹216 (d) ₹72
  36. 36.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹7 (b) ₹63 (c) ₹57 (d) ₹56
  37. 37.If 8 pens cost ₹64, how much do 9 pens cost? (a) ₹576 (b) ₹80 (c) ₹65 (d) ₹72
  38. 38.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹153 (d) ₹136
  39. 39.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹112 (b) ₹16 (c) ₹32 (d) ₹72
  40. 40.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 28 days (d) 7 days

Answer key

  1. ₹30
  2. ₹60
  3. ₹95
  4. 6 days
  5. ₹39
  6. ₹153
  7. ₹90
  8. ₹220
  9. ₹39
  10. ₹16
  11. 16 days
  12. 18 days
  13. ₹48
  14. ₹18
  15. 3 days
  16. ₹190
  17. 12 days
  18. ₹145
  19. ₹81
  20. ₹56
  21. ₹40
  22. ₹72
  23. 28 days
  24. ₹35
  25. ₹126
  26. ₹304
  27. ₹240
  28. 21 days
  29. ₹100
  30. ₹60
  31. ₹75
  32. ₹66
  33. ₹168
  34. ₹21
  35. ₹72
  36. ₹56
  37. ₹72
  38. ₹136
  39. ₹112
  40. 7 days

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