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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 115 · 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.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹117 (b) ₹162 (c) ₹18 (d) ₹72
  2. 2.4 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
  3. 3.₹204 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹85 (d) ₹119
  4. 4.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 7 days
  5. 5.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 3 days (d) 12 days
  6. 6.₹182 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹65 (b) ₹13 (c) ₹117 (d) ₹91
  7. 7.If 9 mangoes cost ₹180, how much do 7 mangoes cost? (a) ₹160 (b) ₹1260 (c) ₹140 (d) ₹178
  8. 8.If 3 notebooks cost ₹9, how much do 7 notebooks cost? (a) ₹13 (b) ₹63 (c) ₹24 (d) ₹21
  9. 9.If 9 kites cost ₹27, how much do 3 kites cost? (a) ₹12 (b) ₹81 (c) ₹9 (d) ₹21
  10. 10.If 5 pens cost ₹95, how much do 12 pens cost? (a) ₹102 (b) ₹228 (c) ₹247 (d) ₹1140
  11. 11.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 20 days (c) 12 days (d) 8 days
  12. 12.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹60 (c) ₹108 (d) ₹12
  13. 13.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
  14. 14.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 17 days (d) 9 days
  15. 15.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 3 days
  16. 16.₹468 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹36 (b) ₹234 (c) ₹288 (d) ₹180
  17. 17.If 3 mangoes cost ₹21, how much do 4 mangoes cost? (a) ₹84 (b) ₹28 (c) ₹22 (d) ₹35
  18. 18.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 4 days
  19. 19.If 9 kites cost ₹63, how much do 4 kites cost? (a) ₹28 (b) ₹252 (c) ₹35 (d) ₹58
  20. 20.If 7 mangoes cost ₹168, how much do 4 mangoes cost? (a) ₹120 (b) ₹672 (c) ₹96 (d) ₹165
  21. 21.If 7 mangoes cost ₹49, how much do 8 mangoes cost? (a) ₹50 (b) ₹392 (c) ₹63 (d) ₹56
  22. 22.If 6 pens cost ₹120, how much do 10 pens cost? (a) ₹220 (b) ₹124 (c) ₹1200 (d) ₹200
  23. 23.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹69 (d) ₹46
  24. 24.If 4 notebooks cost ₹16, how much do 8 notebooks cost? (a) ₹32 (b) ₹36 (c) ₹20 (d) ₹128
  25. 25.If 5 mangoes cost ₹45, how much do 8 mangoes cost? (a) ₹360 (b) ₹81 (c) ₹72 (d) ₹48
  26. 26.If 6 pens cost ₹48, how much do 4 pens cost? (a) ₹32 (b) ₹40 (c) ₹192 (d) ₹46
  27. 27.If 2 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹54 (b) ₹108 (c) ₹37 (d) ₹72
  28. 28.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹40 (b) ₹240 (c) ₹140 (d) ₹280
  29. 29.₹240 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹120 (b) ₹96 (c) ₹144 (d) ₹48
  30. 30.If 8 mangoes cost ₹40, how much do 9 mangoes cost? (a) ₹360 (b) ₹50 (c) ₹45 (d) ₹41
  31. 31.If 3 notebooks cost ₹30, how much do 10 notebooks cost? (a) ₹300 (b) ₹100 (c) ₹37 (d) ₹110
  32. 32.If 2 notebooks cost ₹6, how much do 5 notebooks cost? (a) ₹30 (b) ₹18 (c) ₹15 (d) ₹9
  33. 33.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 4 days (d) 9 days
  34. 34.If 8 pens cost ₹192, how much do 2 pens cost? (a) ₹384 (b) ₹48 (c) ₹186 (d) ₹72
  35. 35.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 7 days (d) 13 days
  36. 36.If 4 mangoes cost ₹20, how much do 12 mangoes cost? (a) ₹28 (b) ₹60 (c) ₹240 (d) ₹65
  37. 37.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 26 days (d) 27 days
  38. 38.If 5 kites cost ₹30, how much do 4 kites cost? (a) ₹30 (b) ₹24 (c) ₹29 (d) ₹120
  39. 39.If 9 kites cost ₹90, how much do 6 kites cost? (a) ₹70 (b) ₹60 (c) ₹87 (d) ₹540
  40. 40.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹11 (c) ₹22 (d) ₹33

Answer key

  1. ₹162
  2. 4 days
  3. ₹119
  4. 8 days
  5. 3 days
  6. ₹117
  7. ₹140
  8. ₹21
  9. ₹9
  10. ₹228
  11. 20 days
  12. ₹108
  13. 3 days
  14. 39 days
  15. 21 days
  16. ₹288
  17. ₹28
  18. 5 days
  19. ₹28
  20. ₹96
  21. ₹56
  22. ₹200
  23. ₹69
  24. ₹32
  25. ₹72
  26. ₹32
  27. ₹54
  28. ₹240
  29. ₹144
  30. ₹45
  31. ₹100
  32. ₹15
  33. 9 days
  34. ₹48
  35. 5 days
  36. ₹60
  37. 27 days
  38. ₹24
  39. ₹60
  40. ₹33

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