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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 98 · 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 4 pens cost ₹24, how much do 3 pens cost? (a) ₹24 (b) ₹72 (c) ₹18 (d) ₹23
  2. 2.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 11 days
  3. 3.If 3 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹160 (b) ₹432 (c) ₹54 (d) ₹144
  4. 4.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹336 (b) ₹240 (c) ₹48 (d) ₹144
  5. 5.If 7 notebooks cost ₹28, how much do 4 notebooks cost? (a) ₹20 (b) ₹112 (c) ₹25 (d) ₹16
  6. 6.7 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) 8 days (d) 7 days
  7. 7.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹25 (b) ₹75 (c) ₹100 (d) ₹125
  8. 8.If 9 pens cost ₹162, how much do 12 pens cost? (a) ₹1944 (b) ₹165 (c) ₹234 (d) ₹216
  9. 9.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹35 (d) ₹5
  10. 10.₹184 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹184 (b) ₹138 (c) ₹92 (d) ₹46
  11. 11.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹117 (b) ₹78 (c) ₹156 (d) ₹39
  12. 12.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹36 (c) ₹18 (d) ₹27
  13. 13.If 9 pens cost ₹36, how much do 12 pens cost? (a) ₹48 (b) ₹39 (c) ₹432 (d) ₹52
  14. 14.₹286 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹143 (d) ₹156
  15. 15.If 5 mangoes cost ₹30, how much do 3 mangoes cost? (a) ₹90 (b) ₹18 (c) ₹24 (d) ₹28
  16. 16.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 1 day (d) 37 days
  17. 17.If 9 kites cost ₹99, how much do 6 kites cost? (a) ₹594 (b) ₹66 (c) ₹77 (d) ₹96
  18. 18.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹15 (b) ₹35 (c) ₹25 (d) ₹5
  19. 19.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days
  20. 20.7 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) 3 days (d) 7 days
  21. 21.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹170 (b) ₹204 (c) ₹238 (d) ₹34
  22. 22.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹115 (d) ₹23
  23. 23.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹125 (b) ₹100 (c) ₹300 (d) ₹76
  24. 24.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹13 (b) ₹117 (c) ₹91 (d) ₹65
  25. 25.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 28 days (c) 13 days (d) 27 days
  26. 26.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹72 (d) ₹80
  27. 27.If 3 mangoes cost ₹33, how much do 5 mangoes cost? (a) ₹35 (b) ₹165 (c) ₹66 (d) ₹55
  28. 28.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days
  29. 29.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 22 days (d) 21 days
  30. 30.If 7 notebooks cost ₹35, how much do 11 notebooks cost? (a) ₹39 (b) ₹55 (c) ₹60 (d) ₹385
  31. 31.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹184 (d) ₹161
  32. 32.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 7 days (c) 63 days (d) 21 days
  33. 33.If 5 kites cost ₹75, how much do 4 kites cost? (a) ₹75 (b) ₹60 (c) ₹74 (d) ₹300
  34. 34.If 6 pens cost ₹126, how much do 7 pens cost? (a) ₹147 (b) ₹168 (c) ₹882 (d) ₹127
  35. 35.If 3 notebooks cost ₹21, how much do 5 notebooks cost? (a) ₹35 (b) ₹105 (c) ₹23 (d) ₹42
  36. 36.If 9 kites cost ₹162, how much do 5 kites cost? (a) ₹108 (b) ₹90 (c) ₹158 (d) ₹810
  37. 37.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 6 days (d) 10 days
  38. 38.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹315 (b) ₹350 (c) ₹35 (d) ₹175
  39. 39.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 3 days (d) 2 days
  40. 40.If 4 mangoes cost ₹28, how much do 12 mangoes cost? (a) ₹36 (b) ₹91 (c) ₹336 (d) ₹84

Answer key

  1. ₹18
  2. 6 days
  3. ₹144
  4. ₹336
  5. ₹16
  6. 7 days
  7. ₹100
  8. ₹216
  9. ₹35
  10. ₹138
  11. ₹117
  12. ₹36
  13. ₹48
  14. ₹156
  15. ₹18
  16. 36 days
  17. ₹66
  18. ₹35
  19. 8 days
  20. 7 days
  21. ₹238
  22. ₹115
  23. ₹100
  24. ₹117
  25. 27 days
  26. ₹80
  27. ₹55
  28. 3 days
  29. 21 days
  30. ₹55
  31. ₹184
  32. 63 days
  33. ₹60
  34. ₹147
  35. ₹35
  36. ₹90
  37. 16 days
  38. ₹315
  39. 2 days
  40. ₹84

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