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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 741 · 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.₹440 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹440 (b) ₹220 (c) ₹44 (d) ₹396
  2. 2.If 8 mangoes cost ₹192, how much do 4 mangoes cost? (a) ₹120 (b) ₹768 (c) ₹96 (d) ₹188
  3. 3.If 5 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹39 (b) ₹36 (c) ₹22 (d) ₹180
  4. 4.If 8 pens cost ₹56, how much do 2 pens cost? (a) ₹112 (b) ₹21 (c) ₹50 (d) ₹14
  5. 5.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹35 (b) ₹175 (c) ₹350 (d) ₹315
  6. 6.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
  7. 7.If 9 notebooks cost ₹126, how much do 11 notebooks cost? (a) ₹128 (b) ₹154 (c) ₹168 (d) ₹1386
  8. 8.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹144 (b) ₹168 (c) ₹192 (d) ₹48
  9. 9.If 9 pens cost ₹225, how much do 6 pens cost? (a) ₹222 (b) ₹175 (c) ₹150 (d) ₹1350
  10. 10.If 7 notebooks cost ₹56, how much do 11 notebooks cost? (a) ₹616 (b) ₹96 (c) ₹60 (d) ₹88
  11. 11.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹52 (b) ₹78 (c) ₹26 (d) ₹39
  12. 12.If 4 mangoes cost ₹88, how much do 2 mangoes cost? (a) ₹176 (b) ₹86 (c) ₹44 (d) ₹66
  13. 13.If 9 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹432 (b) ₹56 (c) ₹48 (d) ₹69
  14. 14.If 9 pens cost ₹198, how much do 11 pens cost? (a) ₹200 (b) ₹242 (c) ₹264 (d) ₹2178
  15. 15.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 40 days (d) 39 days
  16. 16.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
  17. 17.₹396 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹396 (b) ₹44 (c) ₹352 (d) ₹198
  18. 18.₹451 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹328 (b) ₹369 (c) ₹123 (d) ₹41
  19. 19.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 14 days (d) 6 days
  20. 20.₹112 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹32 (b) ₹56 (c) ₹16 (d) ₹80
  21. 21.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 17 days (d) 10 days
  22. 22.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 16 days (c) 26 days (d) 10 days
  23. 23.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹238 (b) ₹204 (c) ₹170 (d) ₹34
  24. 24.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 16 days (c) 29 days (d) 28 days
  25. 25.If 8 kites cost ₹160, how much do 4 kites cost? (a) ₹100 (b) ₹156 (c) ₹80 (d) ₹640
  26. 26.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 18 days (d) 19 days
  27. 27.If 2 pens cost ₹28, how much do 3 pens cost? (a) ₹29 (b) ₹56 (c) ₹84 (d) ₹42
  28. 28.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹148 (b) ₹222 (c) ₹185 (d) ₹37
  29. 29.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹128 (b) ₹160 (c) ₹144 (d) ₹32
  30. 30.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹96 (b) ₹264 (c) ₹432 (d) ₹48
  31. 31.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹53 (d) ₹52
  32. 32.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹66 (d) ₹55
  33. 33.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹200 (b) ₹250 (c) ₹50 (d) ₹150
  34. 34.₹140 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹105 (b) ₹70 (c) ₹140 (d) ₹35
  35. 35.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 18 days (b) 5 days (c) 3 days (d) 4 days
  36. 36.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹150 (d) ₹175
  37. 37.If 7 notebooks cost ₹63, how much do 5 notebooks cost? (a) ₹61 (b) ₹315 (c) ₹45 (d) ₹54
  38. 38.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹90 (d) ₹50
  39. 39.If 2 kites cost ₹10, how much do 4 kites cost? (a) ₹12 (b) ₹25 (c) ₹40 (d) ₹20
  40. 40.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 28 days (d) 7 days

Answer key

  1. ₹396
  2. ₹96
  3. ₹36
  4. ₹14
  5. ₹315
  6. 25 days
  7. ₹154
  8. ₹192
  9. ₹150
  10. ₹88
  11. ₹52
  12. ₹44
  13. ₹48
  14. ₹242
  15. 39 days
  16. 3 days
  17. ₹352
  18. ₹328
  19. 30 days
  20. ₹80
  21. 16 days
  22. 26 days
  23. ₹238
  24. 28 days
  25. ₹80
  26. 18 days
  27. ₹42
  28. ₹185
  29. ₹160
  30. ₹432
  31. ₹52
  32. ₹66
  33. ₹250
  34. ₹105
  35. 4 days
  36. ₹150
  37. ₹45
  38. ₹90
  39. ₹20
  40. 7 days

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