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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 455 · 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. 1.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 17 days (c) 12 days (d) 4 days
  2. 2.If 5 pens cost ₹125, how much do 8 pens cost? (a) ₹200 (b) ₹225 (c) ₹1000 (d) ₹128
  3. 3.If 3 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹220 (b) ₹600 (c) ₹67 (d) ₹200
  4. 4.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹138 (d) ₹139
  5. 5.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 1 day (d) 13 days
  6. 6.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹192 (b) ₹32 (c) ₹112 (d) ₹224
  7. 7.If 3 notebooks cost ₹63, how much do 11 notebooks cost? (a) ₹693 (b) ₹71 (c) ₹231 (d) ₹252
  8. 8.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 2 days (d) 4 days
  9. 9.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 5 days
  10. 10.If 9 pens cost ₹144, how much do 5 pens cost? (a) ₹80 (b) ₹720 (c) ₹96 (d) ₹140
  11. 11.₹231 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹21 (b) ₹63 (c) ₹189 (d) ₹168
  12. 12.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 24 days (d) 18 days
  13. 13.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 14 days
  14. 14.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 8 days (d) 14 days
  15. 15.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹243 (b) ₹27 (c) ₹108 (d) ₹270
  16. 16.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹20 (c) ₹10 (d) ₹5
  17. 17.If 6 kites cost ₹24, how much do 12 kites cost? (a) ₹30 (b) ₹52 (c) ₹48 (d) ₹288
  18. 18.If 3 kites cost ₹21, how much do 9 kites cost? (a) ₹27 (b) ₹70 (c) ₹189 (d) ₹63
  19. 19.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 2 days
  20. 20.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 11 days (d) 12 days
  21. 21.If 2 pens cost ₹48, how much do 4 pens cost? (a) ₹50 (b) ₹96 (c) ₹120 (d) ₹192
  22. 22.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 3 days
  23. 23.If 8 kites cost ₹120, how much do 6 kites cost? (a) ₹720 (b) ₹118 (c) ₹105 (d) ₹90
  24. 24.If 8 pens cost ₹184, how much do 10 pens cost? (a) ₹1840 (b) ₹253 (c) ₹186 (d) ₹230
  25. 25.₹114 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹114 (b) ₹76 (c) ₹57 (d) ₹38
  26. 26.₹644 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹414 (d) ₹322
  27. 27.If 4 pens cost ₹36, how much do 3 pens cost? (a) ₹35 (b) ₹27 (c) ₹108 (d) ₹36
  28. 28.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹78 (b) ₹91 (c) ₹65 (d) ₹13
  29. 29.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 19 days (c) 2 days (d) 18 days
  30. 30.If 5 pens cost ₹115, how much do 4 pens cost? (a) ₹92 (b) ₹460 (c) ₹114 (d) ₹115
  31. 31.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 10 days (d) 9 days
  32. 32.If 4 pens cost ₹88, how much do 7 pens cost? (a) ₹616 (b) ₹91 (c) ₹176 (d) ₹154
  33. 33.If 2 kites cost ₹36, how much do 5 kites cost? (a) ₹90 (b) ₹39 (c) ₹180 (d) ₹108
  34. 34.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 48 days (c) 18 days (d) 6 days
  35. 35.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹288 (d) ₹198
  36. 36.If 4 kites cost ₹60, how much do 8 kites cost? (a) ₹480 (b) ₹135 (c) ₹120 (d) ₹64
  37. 37.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹252 (b) ₹48 (c) ₹37 (d) ₹42
  38. 38.If 2 mangoes cost ₹34, how much do 9 mangoes cost? (a) ₹41 (b) ₹306 (c) ₹153 (d) ₹170
  39. 39.If 2 mangoes cost ₹40, how much do 4 mangoes cost? (a) ₹100 (b) ₹42 (c) ₹160 (d) ₹80
  40. 40.If 6 notebooks cost ₹66, how much do 4 notebooks cost? (a) ₹64 (b) ₹264 (c) ₹55 (d) ₹44

Answer key

  1. 16 days
  2. ₹200
  3. ₹200
  4. ₹138
  5. 1 day
  6. ₹192
  7. ₹231
  8. 3 days
  9. 3 days
  10. ₹80
  11. ₹168
  12. 24 days
  13. 15 days
  14. 14 days
  15. ₹243
  16. ₹15
  17. ₹48
  18. ₹63
  19. 8 days
  20. 12 days
  21. ₹96
  22. 7 days
  23. ₹90
  24. ₹230
  25. ₹76
  26. ₹414
  27. ₹27
  28. ₹91
  29. 18 days
  30. ₹92
  31. 9 days
  32. ₹154
  33. ₹90
  34. 48 days
  35. ₹288
  36. ₹120
  37. ₹42
  38. ₹153
  39. ₹80
  40. ₹44

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