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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 54 · 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 5 kites cost ₹125, how much do 7 kites cost? (a) ₹875 (b) ₹127 (c) ₹200 (d) ₹175
  2. 2.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹49 (b) ₹393 (c) ₹392 (d) ₹441
  3. 3.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 14 days (d) 15 days
  4. 4.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 6 days (d) 5 days
  5. 5.If 5 notebooks cost ₹120, how much do 3 notebooks cost? (a) ₹72 (b) ₹96 (c) ₹360 (d) ₹118
  6. 6.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹18 (b) ₹108 (c) ₹99 (d) ₹90
  7. 7.If 6 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹32 (b) ₹36 (c) ₹26 (d) ₹192
  8. 8.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹8 (d) ₹40
  9. 9.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
  10. 10.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 3 days (d) 4 days
  11. 11.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 3 days (d) 27 days
  12. 12.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 1 day (d) 2 days
  13. 13.If 7 kites cost ₹70, how much do 5 kites cost? (a) ₹50 (b) ₹60 (c) ₹68 (d) ₹350
  14. 14.If 8 notebooks cost ₹32, how much do 3 notebooks cost? (a) ₹12 (b) ₹27 (c) ₹96 (d) ₹16
  15. 15.If 7 pens cost ₹140, how much do 9 pens cost? (a) ₹142 (b) ₹200 (c) ₹1260 (d) ₹180
  16. 16.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹26 (b) ₹52 (c) ₹13 (d) ₹39
  17. 17.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 6 days
  18. 18.If 6 notebooks cost ₹114, how much do 7 notebooks cost? (a) ₹798 (b) ₹152 (c) ₹133 (d) ₹115
  19. 19.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 7 days (d) 5 days
  20. 20.If 4 notebooks cost ₹32, how much do 5 notebooks cost? (a) ₹33 (b) ₹40 (c) ₹160 (d) ₹48
  21. 21.If 8 pens cost ₹32, how much do 6 pens cost? (a) ₹24 (b) ₹28 (c) ₹30 (d) ₹192
  22. 22.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹8 (b) ₹72 (c) ₹16 (d) ₹44
  23. 23.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹87 (b) ₹145 (c) ₹116 (d) ₹29
  24. 24.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 13 days (d) 27 days
  25. 25.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 13 days (d) 11 days
  26. 26.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 3 days
  27. 27.If 5 notebooks cost ₹95, how much do 6 notebooks cost? (a) ₹114 (b) ₹133 (c) ₹96 (d) ₹570
  28. 28.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹96 (d) ₹192
  29. 29.If 3 kites cost ₹30, how much do 9 kites cost? (a) ₹36 (b) ₹100 (c) ₹90 (d) ₹270
  30. 30.₹140 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹70 (b) ₹20 (c) ₹140 (d) ₹120
  31. 31.If 2 kites cost ₹46, how much do 12 kites cost? (a) ₹552 (b) ₹299 (c) ₹56 (d) ₹276
  32. 32.If 7 kites cost ₹70, how much do 6 kites cost? (a) ₹70 (b) ₹420 (c) ₹60 (d) ₹69
  33. 33.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 5 days
  34. 34.If 9 mangoes cost ₹126, how much do 11 mangoes cost? (a) ₹1386 (b) ₹154 (c) ₹168 (d) ₹128
  35. 35.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹63 (b) ₹56 (c) ₹7 (d) ₹35
  36. 36.If 7 mangoes cost ₹49, how much do 2 mangoes cost? (a) ₹98 (b) ₹44 (c) ₹21 (d) ₹14
  37. 37.₹40 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹10 (d) ₹30
  38. 38.If 3 mangoes cost ₹9, how much do 4 mangoes cost? (a) ₹15 (b) ₹10 (c) ₹36 (d) ₹12
  39. 39.₹154 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹84 (d) ₹77
  40. 40.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹12 (b) ₹48 (c) ₹36 (d) ₹24

Answer key

  1. ₹175
  2. ₹392
  3. 14 days
  4. 5 days
  5. ₹72
  6. ₹108
  7. ₹32
  8. ₹40
  9. 49 days
  10. 4 days
  11. 27 days
  12. 2 days
  13. ₹50
  14. ₹12
  15. ₹180
  16. ₹39
  17. 5 days
  18. ₹133
  19. 6 days
  20. ₹40
  21. ₹24
  22. ₹72
  23. ₹145
  24. 27 days
  25. 9 days
  26. 6 days
  27. ₹114
  28. ₹144
  29. ₹90
  30. ₹120
  31. ₹276
  32. ₹60
  33. 7 days
  34. ₹154
  35. ₹56
  36. ₹14
  37. ₹30
  38. ₹12
  39. ₹84
  40. ₹36

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