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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 954 · 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. 1.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 16 days
  2. 2.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹220 (b) ₹40 (c) ₹240 (d) ₹200
  3. 3.If 4 mangoes cost ₹68, how much do 6 mangoes cost? (a) ₹408 (b) ₹119 (c) ₹102 (d) ₹70
  4. 4.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 19 days (c) 21 days (d) 11 days
  5. 5.If 2 mangoes cost ₹22, how much do 11 mangoes cost? (a) ₹121 (b) ₹31 (c) ₹132 (d) ₹242
  6. 6.If 2 kites cost ₹34, how much do 3 kites cost? (a) ₹35 (b) ₹68 (c) ₹102 (d) ₹51
  7. 7.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 4 days (c) 12 days (d) 17 days
  8. 8.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 9 days (d) 4 days
  9. 9.If 6 kites cost ₹24, how much do 4 kites cost? (a) ₹96 (b) ₹20 (c) ₹22 (d) ₹16
  10. 10.If 7 pens cost ₹91, how much do 9 pens cost? (a) ₹117 (b) ₹819 (c) ₹93 (d) ₹130
  11. 11.If 8 pens cost ₹64, how much do 11 pens cost? (a) ₹96 (b) ₹88 (c) ₹704 (d) ₹67
  12. 12.If 2 notebooks cost ₹12, how much do 10 notebooks cost? (a) ₹120 (b) ₹20 (c) ₹66 (d) ₹60
  13. 13.If 5 pens cost ₹90, how much do 3 pens cost? (a) ₹54 (b) ₹88 (c) ₹72 (d) ₹270
  14. 14.₹385 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹140 (d) ₹280
  15. 15.If 8 notebooks cost ₹144, how much do 4 notebooks cost? (a) ₹90 (b) ₹140 (c) ₹576 (d) ₹72
  16. 16.If 3 pens cost ₹75, how much do 10 pens cost? (a) ₹250 (b) ₹275 (c) ₹750 (d) ₹82
  17. 17.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹16 (b) ₹64 (c) ₹80 (d) ₹72
  18. 18.If 6 pens cost ₹84, how much do 12 pens cost? (a) ₹182 (b) ₹90 (c) ₹1008 (d) ₹168
  19. 19.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 9 days (d) 15 days
  20. 20.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 17 days (c) 7 days (d) 32 days
  21. 21.If 6 notebooks cost ₹126, how much do 10 notebooks cost? (a) ₹130 (b) ₹231 (c) ₹1260 (d) ₹210
  22. 22.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 23 days (c) 7 days (d) 22 days
  23. 23.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹128 (b) ₹144 (c) ₹160 (d) ₹32
  24. 24.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹210 (b) ₹135 (c) ₹60 (d) ₹30
  25. 25.If 4 pens cost ₹32, how much do 9 pens cost? (a) ₹72 (b) ₹37 (c) ₹80 (d) ₹288
  26. 26.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 2 days (d) 9 days
  27. 27.If 7 pens cost ₹21, how much do 4 pens cost? (a) ₹18 (b) ₹84 (c) ₹15 (d) ₹12
  28. 28.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 25 days (d) 9 days
  29. 29.If 9 kites cost ₹171, how much do 5 kites cost? (a) ₹114 (b) ₹95 (c) ₹855 (d) ₹167
  30. 30.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹55 (d) ₹80
  31. 31.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹54 (d) ₹45
  32. 32.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 16 days (c) 4 days (d) 41 days
  33. 33.If 7 kites cost ₹35, how much do 3 kites cost? (a) ₹20 (b) ₹31 (c) ₹105 (d) ₹15
  34. 34.If 3 notebooks cost ₹33, how much do 8 notebooks cost? (a) ₹38 (b) ₹264 (c) ₹88 (d) ₹99
  35. 35.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹232 (b) ₹29 (c) ₹203 (d) ₹116
  36. 36.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 11 days (d) 15 days
  37. 37.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹72 (b) ₹12 (c) ₹66 (d) ₹60
  38. 38.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 12 days
  39. 39.If 5 kites cost ₹15, how much do 12 kites cost? (a) ₹39 (b) ₹180 (c) ₹36 (d) ₹22
  40. 40.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 17 days (d) 22 days

Answer key

  1. 6 days
  2. ₹240
  3. ₹102
  4. 20 days
  5. ₹121
  6. ₹51
  7. 16 days
  8. 49 days
  9. ₹16
  10. ₹117
  11. ₹88
  12. ₹60
  13. ₹54
  14. ₹245
  15. ₹72
  16. ₹250
  17. ₹80
  18. ₹168
  19. 21 days
  20. 32 days
  21. ₹210
  22. 22 days
  23. ₹160
  24. ₹210
  25. ₹72
  26. 8 days
  27. ₹12
  28. 25 days
  29. ₹95
  30. ₹80
  31. ₹45
  32. 40 days
  33. ₹15
  34. ₹88
  35. ₹203
  36. 14 days
  37. ₹72
  38. 8 days
  39. ₹36
  40. 21 days

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