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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 532 · 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. 1.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 13 days
  2. 2.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 4 days (d) 9 days
  3. 3.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹40 (b) ₹10 (c) ₹50 (d) ₹25
  4. 4.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹7 (b) ₹56 (c) ₹49 (d) ₹14
  5. 5.If 5 pens cost ₹75, how much do 12 pens cost? (a) ₹82 (b) ₹195 (c) ₹900 (d) ₹180
  6. 6.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 14 days
  7. 7.If 4 pens cost ₹68, how much do 11 pens cost? (a) ₹748 (b) ₹204 (c) ₹187 (d) ₹75
  8. 8.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 9 days (d) 7 days
  9. 9.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 7 days (d) 2 days
  10. 10.If 9 kites cost ₹126, how much do 10 kites cost? (a) ₹140 (b) ₹1260 (c) ₹154 (d) ₹127
  11. 11.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹136 (b) ₹119 (c) ₹68 (d) ₹17
  12. 12.If 5 mangoes cost ₹95, how much do 12 mangoes cost? (a) ₹247 (b) ₹228 (c) ₹102 (d) ₹1140
  13. 13.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
  14. 14.₹294 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹105 (b) ₹189 (c) ₹147 (d) ₹21
  15. 15.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 15 days (c) 11 days (d) 27 days
  16. 16.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹43 (b) ₹86 (c) ₹387 (d) ₹430
  17. 17.If 5 mangoes cost ₹25, how much do 2 mangoes cost? (a) ₹10 (b) ₹15 (c) ₹22 (d) ₹50
  18. 18.If 3 mangoes cost ₹15, how much do 11 mangoes cost? (a) ₹165 (b) ₹60 (c) ₹23 (d) ₹55
  19. 19.If 9 kites cost ₹180, how much do 3 kites cost? (a) ₹80 (b) ₹60 (c) ₹174 (d) ₹540
  20. 20.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 7 days (d) 9 days
  21. 21.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 9 days (d) 4 days
  22. 22.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹135 (b) ₹91 (c) ₹45 (d) ₹90
  23. 23.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹16 (b) ₹48 (c) ₹96 (d) ₹80
  24. 24.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 48 days (b) 4 days (c) 21 days (d) 3 days
  25. 25.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 7 days (d) 6 days
  26. 26.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹125 (c) ₹25 (d) ₹200
  27. 27.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 3 days (c) 9 days (d) 15 days
  28. 28.If 7 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹20 (b) ₹140 (c) ₹24 (d) ₹26
  29. 29.If 8 mangoes cost ₹168, how much do 12 mangoes cost? (a) ₹252 (b) ₹172 (c) ₹273 (d) ₹2016
  30. 30.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 6 days (c) 5 days (d) 20 days
  31. 31.₹275 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹25 (b) ₹75 (c) ₹225 (d) ₹200
  32. 32.If 6 kites cost ₹18, how much do 7 kites cost? (a) ₹24 (b) ₹19 (c) ₹21 (d) ₹126
  33. 33.If 3 pens cost ₹72, how much do 6 pens cost? (a) ₹144 (b) ₹432 (c) ₹168 (d) ₹75
  34. 34.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹208 (c) ₹169 (d) ₹26
  35. 35.If 3 kites cost ₹72, how much do 6 kites cost? (a) ₹75 (b) ₹168 (c) ₹144 (d) ₹432
  36. 36.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 4 days (c) 16 days (d) 5 days
  37. 37.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹75 (b) ₹105 (c) ₹15 (d) ₹90
  38. 38.If 6 pens cost ₹150, how much do 4 pens cost? (a) ₹125 (b) ₹100 (c) ₹148 (d) ₹600
  39. 39.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 9 days (d) 13 days
  40. 40.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 9 days (d) 8 days

Answer key

  1. 9 days
  2. 49 days
  3. ₹40
  4. ₹49
  5. ₹180
  6. 6 days
  7. ₹187
  8. 8 days
  9. 8 days
  10. ₹140
  11. ₹119
  12. ₹228
  13. 27 days
  14. ₹189
  15. 26 days
  16. ₹387
  17. ₹10
  18. ₹55
  19. ₹60
  20. 9 days
  21. 3 days
  22. ₹90
  23. ₹80
  24. 3 days
  25. 6 days
  26. ₹200
  27. 15 days
  28. ₹20
  29. ₹252
  30. 5 days
  31. ₹200
  32. ₹21
  33. ₹144
  34. ₹208
  35. ₹144
  36. 5 days
  37. ₹105
  38. ₹100
  39. 25 days
  40. 8 days

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