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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 702 · 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. 1.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 15 days (d) 14 days
  2. 2.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹49 (b) ₹7 (c) ₹35 (d) ₹63
  3. 3.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 1 day (d) 28 days
  4. 4.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 25 days (d) 16 days
  5. 5.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹196 (d) ₹126
  6. 6.If 9 pens cost ₹72, how much do 12 pens cost? (a) ₹96 (b) ₹104 (c) ₹75 (d) ₹864
  7. 7.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 41 days (d) 40 days
  8. 8.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹48 (d) ₹64
  9. 9.If 9 mangoes cost ₹117, how much do 3 mangoes cost? (a) ₹111 (b) ₹351 (c) ₹39 (d) ₹52
  10. 10.If 9 pens cost ₹180, how much do 5 pens cost? (a) ₹176 (b) ₹900 (c) ₹100 (d) ₹120
  11. 11.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹24 (b) ₹16 (c) ₹58 (d) ₹128
  12. 12.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 12 days (d) 2 days
  13. 13.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹54 (b) ₹72 (c) ₹108 (d) ₹36
  14. 14.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹104 (b) ₹13 (c) ₹65 (d) ₹117
  15. 15.If 7 notebooks cost ₹147, how much do 6 notebooks cost? (a) ₹882 (b) ₹146 (c) ₹147 (d) ₹126
  16. 16.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 14 days (d) 10 days
  17. 17.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 7 days (d) 15 days
  18. 18.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹20 (c) ₹5 (d) ₹10
  19. 19.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
  20. 20.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹56 (c) ₹14 (d) ₹42
  21. 21.If 6 mangoes cost ₹150, how much do 4 mangoes cost? (a) ₹125 (b) ₹100 (c) ₹600 (d) ₹148
  22. 22.If 5 pens cost ₹95, how much do 4 pens cost? (a) ₹380 (b) ₹76 (c) ₹95 (d) ₹94
  23. 23.If 8 pens cost ₹160, how much do 10 pens cost? (a) ₹200 (b) ₹162 (c) ₹1600 (d) ₹220
  24. 24.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 22 days (b) 13 days (c) 21 days (d) 5 days
  25. 25.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 25 days (d) 23 days
  26. 26.If 5 mangoes cost ₹95, how much do 3 mangoes cost? (a) ₹285 (b) ₹57 (c) ₹93 (d) ₹76
  27. 27.If 3 pens cost ₹63, how much do 4 pens cost? (a) ₹64 (b) ₹105 (c) ₹252 (d) ₹84
  28. 28.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 7 days (c) 34 days (d) 15 days
  29. 29.If 8 kites cost ₹104, how much do 5 kites cost? (a) ₹101 (b) ₹520 (c) ₹78 (d) ₹65
  30. 30.₹140 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹84 (b) ₹56 (c) ₹28 (d) ₹70
  31. 31.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 9 days (d) 26 days
  32. 32.If 3 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹144 (b) ₹54 (c) ₹432 (d) ₹160
  33. 33.If 4 pens cost ₹100, how much do 8 pens cost? (a) ₹200 (b) ₹104 (c) ₹800 (d) ₹225
  34. 34.If 2 mangoes cost ₹32, how much do 3 mangoes cost? (a) ₹96 (b) ₹48 (c) ₹64 (d) ₹33
  35. 35.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹130 (d) ₹117
  36. 36.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 15 days (c) 9 days (d) 6 days
  37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
  38. 38.₹224 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹112 (b) ₹196 (c) ₹224 (d) ₹28
  39. 39.If 3 mangoes cost ₹57, how much do 6 mangoes cost? (a) ₹342 (b) ₹114 (c) ₹133 (d) ₹60
  40. 40.If 6 notebooks cost ₹96, how much do 12 notebooks cost? (a) ₹208 (b) ₹192 (c) ₹102 (d) ₹1152

Answer key

  1. 14 days
  2. ₹63
  3. 28 days
  4. 4 days
  5. ₹196
  6. ₹96
  7. 40 days
  8. ₹48
  9. ₹39
  10. ₹100
  11. ₹16
  12. 12 days
  13. ₹72
  14. ₹104
  15. ₹126
  16. 14 days
  17. 15 days
  18. ₹15
  19. 3 days
  20. ₹42
  21. ₹100
  22. ₹76
  23. ₹200
  24. 21 days
  25. 24 days
  26. ₹57
  27. ₹84
  28. 33 days
  29. ₹65
  30. ₹84
  31. 26 days
  32. ₹144
  33. ₹200
  34. ₹48
  35. ₹130
  36. 24 days
  37. 3 days
  38. ₹196
  39. ₹114
  40. ₹192

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