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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 959 · 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.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹168 (b) ₹48 (c) ₹144 (d) ₹192
  2. 2.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹18 (b) ₹81 (c) ₹72 (d) ₹90
  3. 3.₹280 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹140 (c) ₹245 (d) ₹280
  4. 4.₹120 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹108 (b) ₹120 (c) ₹12 (d) ₹60
  5. 5.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 14 days (d) 11 days
  6. 6.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 15 days (d) 21 days
  7. 7.If 7 pens cost ₹119, how much do 9 pens cost? (a) ₹153 (b) ₹1071 (c) ₹170 (d) ₹121
  8. 8.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
  9. 9.If 3 mangoes cost ₹57, how much do 6 mangoes cost? (a) ₹60 (b) ₹342 (c) ₹133 (d) ₹114
  10. 10.If 4 pens cost ₹72, how much do 5 pens cost? (a) ₹360 (b) ₹90 (c) ₹73 (d) ₹108
  11. 11.If 9 mangoes cost ₹126, how much do 5 mangoes cost? (a) ₹630 (b) ₹70 (c) ₹84 (d) ₹122
  12. 12.If 2 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹80 (b) ₹70 (c) ₹140 (d) ₹25
  13. 13.If 2 kites cost ₹16, how much do 5 kites cost? (a) ₹19 (b) ₹40 (c) ₹48 (d) ₹80
  14. 14.₹468 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹144 (b) ₹234 (c) ₹36 (d) ₹324
  15. 15.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 4 days (d) 3 days
  16. 16.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 5 days (c) 15 days (d) 35 days
  17. 17.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹24 (d) ₹32
  18. 18.If 3 pens cost ₹24, how much do 6 pens cost? (a) ₹48 (b) ₹56 (c) ₹27 (d) ₹144
  19. 19.If 6 mangoes cost ₹84, how much do 8 mangoes cost? (a) ₹126 (b) ₹86 (c) ₹672 (d) ₹112
  20. 20.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 14 days (d) 8 days
  21. 21.₹119 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹102 (b) ₹34 (c) ₹17 (d) ₹85
  22. 22.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 21 days (d) 13 days
  23. 23.If 7 kites cost ₹154, how much do 4 kites cost? (a) ₹110 (b) ₹151 (c) ₹616 (d) ₹88
  24. 24.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹161 (d) ₹184
  25. 25.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 1 day (c) 11 days (d) 3 days
  26. 26.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹126 (d) ₹162
  27. 27.If 4 mangoes cost ₹68, how much do 6 mangoes cost? (a) ₹102 (b) ₹408 (c) ₹70 (d) ₹119
  28. 28.If 2 pens cost ₹46, how much do 4 pens cost? (a) ₹48 (b) ₹115 (c) ₹92 (d) ₹184
  29. 29.If 7 mangoes cost ₹63, how much do 5 mangoes cost? (a) ₹315 (b) ₹54 (c) ₹45 (d) ₹61
  30. 30.₹63 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹9 (b) ₹45 (c) ₹18 (d) ₹54
  31. 31.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 17 days (d) 32 days
  32. 32.If 8 pens cost ₹128, how much do 6 pens cost? (a) ₹768 (b) ₹112 (c) ₹126 (d) ₹96
  33. 33.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹37 (b) ₹60 (c) ₹144 (d) ₹48
  34. 34.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹377 (b) ₹376 (c) ₹47 (d) ₹423
  35. 35.6 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) 6 days (d) 4 days
  36. 36.If 9 pens cost ₹144, how much do 12 pens cost? (a) ₹192 (b) ₹1728 (c) ₹208 (d) ₹147
  37. 37.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹11 (b) ₹33 (c) ₹55 (d) ₹44
  38. 38.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 15 days (c) 22 days (d) 7 days
  39. 39.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 24 days (d) 15 days
  40. 40.If 4 notebooks cost ₹16, how much do 12 notebooks cost? (a) ₹192 (b) ₹52 (c) ₹48 (d) ₹24

Answer key

  1. ₹192
  2. ₹90
  3. ₹245
  4. ₹108
  5. 14 days
  6. 21 days
  7. ₹153
  8. 25 days
  9. ₹114
  10. ₹90
  11. ₹70
  12. ₹70
  13. ₹40
  14. ₹324
  15. 12 days
  16. 35 days
  17. ₹24
  18. ₹48
  19. ₹112
  20. 8 days
  21. ₹85
  22. 21 days
  23. ₹88
  24. ₹161
  25. 3 days
  26. ₹162
  27. ₹102
  28. ₹92
  29. ₹45
  30. ₹45
  31. 2 days
  32. ₹96
  33. ₹48
  34. ₹376
  35. 6 days
  36. ₹192
  37. ₹55
  38. 22 days
  39. 24 days
  40. ₹48

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