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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 452 · 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 7 kites cost ₹77, how much do 3 kites cost? (a) ₹231 (b) ₹33 (c) ₹73 (d) ₹44
  2. 2.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 12 days (d) 20 days
  3. 3.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 23 days (d) 13 days
  4. 4.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 7 days (d) 8 days
  5. 5.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 45 days (c) 46 days (d) 17 days
  6. 6.If 3 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹78 (b) ₹240 (c) ₹216 (d) ₹648
  7. 7.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 28 days (d) 7 days
  8. 8.If 2 pens cost ₹40, how much do 11 pens cost? (a) ₹49 (b) ₹440 (c) ₹240 (d) ₹220
  9. 9.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days
  10. 10.If 3 pens cost ₹75, how much do 4 pens cost? (a) ₹76 (b) ₹125 (c) ₹100 (d) ₹300
  11. 11.₹414 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹322 (b) ₹207 (c) ₹46 (d) ₹92
  12. 12.If 5 kites cost ₹60, how much do 12 kites cost? (a) ₹67 (b) ₹156 (c) ₹144 (d) ₹720
  13. 13.If 3 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹140 (b) ₹63 (c) ₹360 (d) ₹120
  14. 14.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 8 days (d) 10 days
  15. 15.8 workers can build a wall in 9 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 19 days (c) 18 days (d) 5 days
  16. 16.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹441 (d) ₹343
  17. 17.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 11 days (d) 13 days
  18. 18.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 3 days (d) 10 days
  19. 19.If 5 mangoes cost ₹95, how much do 6 mangoes cost? (a) ₹133 (b) ₹570 (c) ₹96 (d) ₹114
  20. 20.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹180 (b) ₹405 (c) ₹450 (d) ₹45
  21. 21.If 3 pens cost ₹72, how much do 2 pens cost? (a) ₹144 (b) ₹48 (c) ₹72 (d) ₹71
  22. 22.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹84 (d) ₹63
  23. 23.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 15 days (d) 34 days
  24. 24.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 13 days (d) 12 days
  25. 25.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 8 days (d) 10 days
  26. 26.If 8 pens cost ₹128, how much do 3 pens cost? (a) ₹384 (b) ₹48 (c) ₹123 (d) ₹64
  27. 27.If 9 pens cost ₹207, how much do 6 pens cost? (a) ₹1242 (b) ₹138 (c) ₹204 (d) ₹161
  28. 28.If 6 notebooks cost ₹102, how much do 4 notebooks cost? (a) ₹85 (b) ₹100 (c) ₹408 (d) ₹68
  29. 29.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
  30. 30.If 7 mangoes cost ₹140, how much do 11 mangoes cost? (a) ₹1540 (b) ₹240 (c) ₹144 (d) ₹220
  31. 31.If 7 mangoes cost ₹147, how much do 2 mangoes cost? (a) ₹42 (b) ₹63 (c) ₹294 (d) ₹142
  32. 32.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹160 (b) ₹40 (c) ₹140 (d) ₹120
  33. 33.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 17 days (d) 7 days
  34. 34.If 4 pens cost ₹44, how much do 11 pens cost? (a) ₹121 (b) ₹484 (c) ₹132 (d) ₹51
  35. 35.If 8 pens cost ₹136, how much do 7 pens cost? (a) ₹952 (b) ₹135 (c) ₹119 (d) ₹136
  36. 36.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 14 days (d) 32 days
  37. 37.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 12 days
  38. 38.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹132 (b) ₹24 (c) ₹168 (d) ₹96
  39. 39.If 9 kites cost ₹108, how much do 5 kites cost? (a) ₹104 (b) ₹72 (c) ₹540 (d) ₹60
  40. 40.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹8 (d) ₹32

Answer key

  1. ₹33
  2. 20 days
  3. 22 days
  4. 8 days
  5. 45 days
  6. ₹216
  7. 28 days
  8. ₹220
  9. 45 days
  10. ₹100
  11. ₹322
  12. ₹144
  13. ₹120
  14. 9 days
  15. 18 days
  16. ₹441
  17. 10 days
  18. 2 days
  19. ₹114
  20. ₹405
  21. ₹48
  22. ₹63
  23. 33 days
  24. 12 days
  25. 10 days
  26. ₹48
  27. ₹138
  28. ₹68
  29. 9 days
  30. ₹220
  31. ₹42
  32. ₹160
  33. 42 days
  34. ₹121
  35. ₹119
  36. 32 days
  37. 6 days
  38. ₹168
  39. ₹60
  40. ₹32

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