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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 578 · 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 4 mangoes cost ₹32, how much do 5 mangoes cost? (a) ₹40 (b) ₹48 (c) ₹33 (d) ₹160
  2. 2.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 4 days (d) 9 days
  3. 3.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹60 (b) ₹84 (c) ₹12 (d) ₹108
  4. 4.If 3 notebooks cost ₹57, how much do 5 notebooks cost? (a) ₹285 (b) ₹114 (c) ₹59 (d) ₹95
  5. 5.If 3 pens cost ₹57, how much do 4 pens cost? (a) ₹95 (b) ₹58 (c) ₹76 (d) ₹228
  6. 6.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 12 days (d) 3 days
  7. 7.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 22 days (d) 21 days
  8. 8.If 6 kites cost ₹36, how much do 8 kites cost? (a) ₹54 (b) ₹48 (c) ₹38 (d) ₹288
  9. 9.If 8 notebooks cost ₹200, how much do 11 notebooks cost? (a) ₹275 (b) ₹203 (c) ₹2200 (d) ₹300
  10. 10.If 8 mangoes cost ₹56, how much do 4 mangoes cost? (a) ₹35 (b) ₹28 (c) ₹52 (d) ₹224
  11. 11.If 8 notebooks cost ₹176, how much do 4 notebooks cost? (a) ₹88 (b) ₹110 (c) ₹704 (d) ₹172
  12. 12.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹7 (c) ₹63 (d) ₹35
  13. 13.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 14 days (c) 16 days (d) 13 days
  14. 14.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹20 (b) ₹8 (c) ₹32 (d) ₹40
  15. 15.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  16. 16.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹20 (b) ₹50 (c) ₹5 (d) ₹45
  17. 17.₹91 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹39 (b) ₹52 (c) ₹13 (d) ₹65
  18. 18.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 6 days (d) 15 days
  19. 19.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 17 days
  20. 20.₹320 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹160 (b) ₹120 (c) ₹40 (d) ₹200
  21. 21.₹258 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹215 (d) ₹258
  22. 22.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹42 (b) ₹21 (c) ₹84 (d) ₹63
  23. 23.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 6 days
  24. 24.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 2 days (d) 8 days
  25. 25.If 8 notebooks cost ₹176, how much do 3 notebooks cost? (a) ₹66 (b) ₹171 (c) ₹528 (d) ₹88
  26. 26.If 9 kites cost ₹189, how much do 7 kites cost? (a) ₹187 (b) ₹1323 (c) ₹168 (d) ₹147
  27. 27.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 6 days (c) 31 days (d) 14 days
  28. 28.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹310 (d) ₹279
  29. 29.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 27 days (d) 28 days
  30. 30.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹325 (d) ₹400
  31. 31.If 2 kites cost ₹32, how much do 10 kites cost? (a) ₹40 (b) ₹176 (c) ₹320 (d) ₹160
  32. 32.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹63 (b) ₹7 (c) ₹28 (d) ₹70
  33. 33.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 39 days (d) 7 days
  34. 34.If 2 pens cost ₹22, how much do 11 pens cost? (a) ₹121 (b) ₹242 (c) ₹132 (d) ₹31
  35. 35.If 4 pens cost ₹96, how much do 11 pens cost? (a) ₹1056 (b) ₹103 (c) ₹264 (d) ₹288
  36. 36.If 5 pens cost ₹75, how much do 3 pens cost? (a) ₹73 (b) ₹225 (c) ₹60 (d) ₹45
  37. 37.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹273 (b) ₹234 (c) ₹39 (d) ₹195
  38. 38.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹76 (d) ₹152
  39. 39.If 2 mangoes cost ₹28, how much do 5 mangoes cost? (a) ₹84 (b) ₹70 (c) ₹140 (d) ₹31
  40. 40.If 2 mangoes cost ₹6, how much do 3 mangoes cost? (a) ₹18 (b) ₹12 (c) ₹9 (d) ₹7

Answer key

  1. ₹40
  2. 4 days
  3. ₹108
  4. ₹95
  5. ₹76
  6. 3 days
  7. 21 days
  8. ₹48
  9. ₹275
  10. ₹28
  11. ₹88
  12. ₹56
  13. 12 days
  14. ₹32
  15. 25 days
  16. ₹45
  17. ₹52
  18. 24 days
  19. 21 days
  20. ₹200
  21. ₹215
  22. ₹63
  23. 6 days
  24. 8 days
  25. ₹66
  26. ₹147
  27. 30 days
  28. ₹279
  29. 27 days
  30. ₹400
  31. ₹160
  32. ₹63
  33. 39 days
  34. ₹121
  35. ₹264
  36. ₹45
  37. ₹234
  38. ₹133
  39. ₹70
  40. ₹9

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