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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 310 · 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 3 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹216 (b) ₹81 (c) ₹72 (d) ₹32
  2. 2.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 17 days (c) 40 days (d) 9 days
  3. 3.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹350 (d) ₹400
  4. 4.If 5 notebooks cost ₹30, how much do 7 notebooks cost? (a) ₹210 (b) ₹32 (c) ₹42 (d) ₹48
  5. 5.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 7 days (d) 4 days
  6. 6.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 6 days (d) 16 days
  7. 7.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 28 days
  8. 8.If 7 kites cost ₹84, how much do 10 kites cost? (a) ₹87 (b) ₹840 (c) ₹120 (d) ₹132
  9. 9.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 16 days (d) 9 days
  10. 10.If 5 kites cost ₹100, how much do 10 kites cost? (a) ₹105 (b) ₹220 (c) ₹200 (d) ₹1000
  11. 11.If 8 pens cost ₹176, how much do 5 pens cost? (a) ₹880 (b) ₹173 (c) ₹132 (d) ₹110
  12. 12.If 6 kites cost ₹138, how much do 12 kites cost? (a) ₹276 (b) ₹144 (c) ₹299 (d) ₹1656
  13. 13.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 12 days
  14. 14.₹495 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹450 (b) ₹90 (c) ₹45 (d) ₹405
  15. 15.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹12 (b) ₹10 (c) ₹36 (d) ₹15
  16. 16.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹100 (c) ₹150 (d) ₹125
  17. 17.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹105 (d) ₹84
  18. 18.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 43 days (c) 10 days (d) 42 days
  19. 19.If 8 pens cost ₹96, how much do 10 pens cost? (a) ₹98 (b) ₹120 (c) ₹132 (d) ₹960
  20. 20.If 3 mangoes cost ₹63, how much do 11 mangoes cost? (a) ₹71 (b) ₹231 (c) ₹693 (d) ₹252
  21. 21.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹132 (b) ₹176 (c) ₹44 (d) ₹88
  22. 22.₹686 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹441 (b) ₹343 (c) ₹49 (d) ₹245
  23. 23.If 3 notebooks cost ₹39, how much do 4 notebooks cost? (a) ₹65 (b) ₹156 (c) ₹40 (d) ₹52
  24. 24.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 2 days
  25. 25.If 9 pens cost ₹90, how much do 5 pens cost? (a) ₹86 (b) ₹450 (c) ₹50 (d) ₹60
  26. 26.₹44 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹33 (d) ₹22
  27. 27.If 9 pens cost ₹207, how much do 12 pens cost? (a) ₹2484 (b) ₹276 (c) ₹299 (d) ₹210
  28. 28.If 8 pens cost ₹112, how much do 11 pens cost? (a) ₹154 (b) ₹115 (c) ₹168 (d) ₹1232
  29. 29.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 3 days (c) 11 days (d) 22 days
  30. 30.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹180 (c) ₹150 (d) ₹165
  31. 31.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹63 (b) ₹36 (c) ₹18 (d) ₹90
  32. 32.If 6 notebooks cost ₹18, how much do 9 notebooks cost? (a) ₹162 (b) ₹27 (c) ₹21 (d) ₹30
  33. 33.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
  34. 34.If 7 notebooks cost ₹126, how much do 8 notebooks cost? (a) ₹162 (b) ₹1008 (c) ₹144 (d) ₹127
  35. 35.₹65 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹5 (b) ₹45 (c) ₹25 (d) ₹40
  36. 36.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 15 days (d) 5 days
  37. 37.If 4 kites cost ₹28, how much do 9 kites cost? (a) ₹70 (b) ₹63 (c) ₹252 (d) ₹33
  38. 38.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹324 (c) ₹180 (d) ₹36
  39. 39.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹36 (b) ₹25 (c) ₹48 (d) ₹72
  40. 40.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 4 days

Answer key

  1. ₹72
  2. 39 days
  3. ₹350
  4. ₹42
  5. 9 days
  6. 16 days
  7. 27 days
  8. ₹120
  9. 15 days
  10. ₹200
  11. ₹110
  12. ₹276
  13. 3 days
  14. ₹405
  15. ₹12
  16. ₹150
  17. ₹84
  18. 42 days
  19. ₹120
  20. ₹231
  21. ₹132
  22. ₹441
  23. ₹52
  24. 8 days
  25. ₹50
  26. ₹33
  27. ₹276
  28. ₹154
  29. 21 days
  30. ₹180
  31. ₹90
  32. ₹27
  33. 4 days
  34. ₹144
  35. ₹40
  36. 5 days
  37. ₹63
  38. ₹324
  39. ₹36
  40. 9 days

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