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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 9 · 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. 1.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 8 days (d) 36 days
  2. 2.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹55 (d) ₹44
  3. 3.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹165 (c) ₹30 (d) ₹180
  4. 4.If 9 mangoes cost ₹36, how much do 12 mangoes cost? (a) ₹432 (b) ₹48 (c) ₹52 (d) ₹39
  5. 5.If 2 kites cost ₹18, how much do 10 kites cost? (a) ₹180 (b) ₹26 (c) ₹99 (d) ₹90
  6. 6.If 3 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹32 (b) ₹264 (c) ₹96 (d) ₹88
  7. 7.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹35 (c) ₹7 (d) ₹49
  8. 8.If 9 kites cost ₹54, how much do 10 kites cost? (a) ₹540 (b) ₹66 (c) ₹55 (d) ₹60
  9. 9.If 4 kites cost ₹48, how much do 2 kites cost? (a) ₹96 (b) ₹36 (c) ₹24 (d) ₹46
  10. 10.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 9 days (c) 13 days (d) 22 days
  11. 11.If 3 pens cost ₹45, how much do 10 pens cost? (a) ₹150 (b) ₹52 (c) ₹450 (d) ₹165
  12. 12.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
  13. 13.If 7 pens cost ₹70, how much do 10 pens cost? (a) ₹110 (b) ₹100 (c) ₹73 (d) ₹700
  14. 14.₹60 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹48 (d) ₹30
  15. 15.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹432 (d) ₹336
  16. 16.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹55 (d) ₹60
  17. 17.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 13 days (d) 14 days
  18. 18.If 9 pens cost ₹27, how much do 4 pens cost? (a) ₹12 (b) ₹22 (c) ₹15 (d) ₹108
  19. 19.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 43 days (d) 42 days
  20. 20.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 1 day (d) 7 days
  21. 21.If 7 mangoes cost ₹21, how much do 6 mangoes cost? (a) ₹18 (b) ₹20 (c) ₹126 (d) ₹21
  22. 22.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 32 days (c) 2 days (d) 33 days
  23. 23.If 7 pens cost ₹119, how much do 5 pens cost? (a) ₹117 (b) ₹102 (c) ₹85 (d) ₹595
  24. 24.If 8 notebooks cost ₹104, how much do 6 notebooks cost? (a) ₹102 (b) ₹78 (c) ₹91 (d) ₹624
  25. 25.If 2 kites cost ₹42, how much do 3 kites cost? (a) ₹84 (b) ₹43 (c) ₹63 (d) ₹126
  26. 26.If 4 notebooks cost ₹88, how much do 10 notebooks cost? (a) ₹220 (b) ₹242 (c) ₹880 (d) ₹94
  27. 27.₹315 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹175 (d) ₹140
  28. 28.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹9 (c) ₹19 (d) ₹27
  29. 29.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹162 (b) ₹189 (c) ₹135 (d) ₹27
  30. 30.₹140 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹70 (b) ₹126 (c) ₹14 (d) ₹140
  31. 31.If 5 mangoes cost ₹125, how much do 6 mangoes cost? (a) ₹175 (b) ₹150 (c) ₹750 (d) ₹126
  32. 32.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 11 days (d) 16 days
  33. 33.If 9 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹65 (b) ₹24 (c) ₹16 (d) ₹144
  34. 34.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 11 days
  35. 35.If 7 notebooks cost ₹119, how much do 5 notebooks cost? (a) ₹102 (b) ₹595 (c) ₹85 (d) ₹117
  36. 36.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 10 days (d) 8 days
  37. 37.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 13 days
  38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 6 days (d) 4 days
  39. 39.If 6 pens cost ₹42, how much do 4 pens cost? (a) ₹35 (b) ₹168 (c) ₹28 (d) ₹40
  40. 40.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹147 (b) ₹98 (c) ₹49 (d) ₹196

Answer key

  1. 36 days
  2. ₹44
  3. ₹180
  4. ₹48
  5. ₹90
  6. ₹88
  7. ₹42
  8. ₹60
  9. ₹24
  10. 22 days
  11. ₹150
  12. 3 days
  13. ₹100
  14. ₹48
  15. ₹432
  16. ₹60
  17. 14 days
  18. ₹12
  19. 42 days
  20. 3 days
  21. ₹18
  22. 32 days
  23. ₹85
  24. ₹78
  25. ₹63
  26. ₹220
  27. ₹175
  28. ₹18
  29. ₹162
  30. ₹126
  31. ₹150
  32. 15 days
  33. ₹16
  34. 6 days
  35. ₹85
  36. 9 days
  37. 5 days
  38. 5 days
  39. ₹28
  40. ₹147

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