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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 458 · 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.₹300 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹150 (b) ₹125 (c) ₹175 (d) ₹25
  2. 2.If 7 notebooks cost ₹147, how much do 4 notebooks cost? (a) ₹84 (b) ₹105 (c) ₹588 (d) ₹144
  3. 3.If 2 pens cost ₹48, how much do 12 pens cost? (a) ₹312 (b) ₹288 (c) ₹576 (d) ₹58
  4. 4.If 3 mangoes cost ₹9, how much do 11 mangoes cost? (a) ₹33 (b) ₹17 (c) ₹99 (d) ₹36
  5. 5.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹200 (b) ₹160 (c) ₹40 (d) ₹180
  6. 6.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 49 days (c) 9 days (d) 19 days
  7. 7.If 2 mangoes cost ₹6, how much do 9 mangoes cost? (a) ₹13 (b) ₹30 (c) ₹54 (d) ₹27
  8. 8.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 19 days (c) 7 days (d) 53 days
  9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 15 days (d) 11 days
  10. 10.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 45 days (d) 21 days
  11. 11.If 4 kites cost ₹16, how much do 12 kites cost? (a) ₹192 (b) ₹48 (c) ₹24 (d) ₹52
  12. 12.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 3 days (d) 12 days
  13. 13.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹33 (b) ₹198 (c) ₹165 (d) ₹132
  14. 14.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 4 days (d) 5 days
  15. 15.If 5 pens cost ₹120, how much do 10 pens cost? (a) ₹264 (b) ₹240 (c) ₹1200 (d) ₹125
  16. 16.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 22 days (c) 14 days (d) 23 days
  17. 17.₹102 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹85 (b) ₹17 (c) ₹51 (d) ₹102
  18. 18.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹92 (b) ₹207 (c) ₹230 (d) ₹23
  19. 19.₹170 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹136 (b) ₹170 (c) ₹85 (d) ₹34
  20. 20.If 4 notebooks cost ₹96, how much do 7 notebooks cost? (a) ₹672 (b) ₹192 (c) ₹168 (d) ₹99
  21. 21.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days
  22. 22.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 4 days (d) 12 days
  23. 23.If 4 pens cost ₹40, how much do 11 pens cost? (a) ₹120 (b) ₹440 (c) ₹110 (d) ₹47
  24. 24.If 7 mangoes cost ₹77, how much do 3 mangoes cost? (a) ₹33 (b) ₹73 (c) ₹44 (d) ₹231
  25. 25.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹57 (b) ₹38 (c) ₹76 (d) ₹19
  26. 26.If 2 pens cost ₹26, how much do 9 pens cost? (a) ₹117 (b) ₹234 (c) ₹33 (d) ₹130
  27. 27.If 6 pens cost ₹132, how much do 5 pens cost? (a) ₹131 (b) ₹660 (c) ₹132 (d) ₹110
  28. 28.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 12 days (d) 7 days
  29. 29.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 9 days (d) 8 days
  30. 30.₹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
  31. 31.If 6 kites cost ₹24, how much do 4 kites cost? (a) ₹20 (b) ₹22 (c) ₹96 (d) ₹16
  32. 32.If 4 mangoes cost ₹36, how much do 11 mangoes cost? (a) ₹99 (b) ₹396 (c) ₹108 (d) ₹43
  33. 33.If 2 notebooks cost ₹34, how much do 12 notebooks cost? (a) ₹408 (b) ₹221 (c) ₹44 (d) ₹204
  34. 34.If 6 kites cost ₹84, how much do 8 kites cost? (a) ₹112 (b) ₹126 (c) ₹86 (d) ₹672
  35. 35.If 2 pens cost ₹8, how much do 12 pens cost? (a) ₹18 (b) ₹48 (c) ₹52 (d) ₹96
  36. 36.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 7 days (d) 15 days
  37. 37.If 2 kites cost ₹36, how much do 4 kites cost? (a) ₹38 (b) ₹90 (c) ₹72 (d) ₹144
  38. 38.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 2 days (d) 3 days
  39. 39.If 2 kites cost ₹38, how much do 5 kites cost? (a) ₹190 (b) ₹41 (c) ₹114 (d) ₹95
  40. 40.If 7 pens cost ₹133, how much do 2 pens cost? (a) ₹128 (b) ₹266 (c) ₹57 (d) ₹38

Answer key

  1. ₹175
  2. ₹84
  3. ₹288
  4. ₹33
  5. ₹200
  6. 49 days
  7. ₹27
  8. 52 days
  9. 26 days
  10. 45 days
  11. ₹48
  12. 3 days
  13. ₹165
  14. 6 days
  15. ₹240
  16. 22 days
  17. ₹85
  18. ₹207
  19. ₹136
  20. ₹168
  21. 25 days
  22. 3 days
  23. ₹110
  24. ₹33
  25. ₹57
  26. ₹117
  27. ₹110
  28. 12 days
  29. 9 days
  30. ₹328
  31. ₹16
  32. ₹99
  33. ₹204
  34. ₹112
  35. ₹48
  36. 15 days
  37. ₹72
  38. 3 days
  39. ₹95
  40. ₹38

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