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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 644 · 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 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 11 days (d) 13 days
  2. 2.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹28 (c) ₹8 (d) ₹32
  3. 3.If 8 notebooks cost ₹184, how much do 4 notebooks cost? (a) ₹92 (b) ₹115 (c) ₹736 (d) ₹180
  4. 4.₹40 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹35 (b) ₹20 (c) ₹5 (d) ₹40
  5. 5.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 7 days (d) 33 days
  6. 6.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹160 (b) ₹220 (c) ₹280 (d) ₹40
  7. 7.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 12 days (d) 18 days
  8. 8.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹18 (b) ₹13 (c) ₹60 (d) ₹15
  9. 9.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹30 (b) ₹18 (c) ₹6 (d) ₹24
  10. 10.₹195 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹39 (b) ₹78 (c) ₹156 (d) ₹117
  11. 11.If 4 kites cost ₹36, how much do 6 kites cost? (a) ₹216 (b) ₹63 (c) ₹38 (d) ₹54
  12. 12.7 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
  13. 13.If 4 mangoes cost ₹96, how much do 9 mangoes cost? (a) ₹216 (b) ₹864 (c) ₹240 (d) ₹101
  14. 14.If 2 notebooks cost ₹24, how much do 3 notebooks cost? (a) ₹72 (b) ₹36 (c) ₹48 (d) ₹25
  15. 15.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 21 days (d) 22 days
  16. 16.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 4 days (d) 5 days
  17. 17.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 9 days (d) 4 days
  18. 18.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹72 (c) ₹8 (d) ₹40
  19. 19.If 6 kites cost ₹60, how much do 3 kites cost? (a) ₹40 (b) ₹57 (c) ₹180 (d) ₹30
  20. 20.If 7 mangoes cost ₹28, how much do 8 mangoes cost? (a) ₹224 (b) ₹32 (c) ₹36 (d) ₹29
  21. 21.If 5 pens cost ₹50, how much do 3 pens cost? (a) ₹48 (b) ₹30 (c) ₹150 (d) ₹40
  22. 22.If 4 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹216 (b) ₹864 (c) ₹234 (d) ₹80
  23. 23.If 4 notebooks cost ₹32, how much do 3 notebooks cost? (a) ₹24 (b) ₹31 (c) ₹96 (d) ₹32
  24. 24.If 9 mangoes cost ₹153, how much do 3 mangoes cost? (a) ₹68 (b) ₹51 (c) ₹459 (d) ₹147
  25. 25.If 3 mangoes cost ₹60, how much do 6 mangoes cost? (a) ₹63 (b) ₹140 (c) ₹120 (d) ₹360
  26. 26.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹189 (d) ₹135
  27. 27.If 7 pens cost ₹42, how much do 9 pens cost? (a) ₹44 (b) ₹60 (c) ₹54 (d) ₹378
  28. 28.If 4 kites cost ₹44, how much do 3 kites cost? (a) ₹33 (b) ₹132 (c) ₹43 (d) ₹44
  29. 29.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 25 days (d) 7 days
  30. 30.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 8 days (d) 6 days
  31. 31.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹120 (b) ₹135 (c) ₹30 (d) ₹150
  32. 32.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 21 days (d) 20 days
  33. 33.If 6 kites cost ₹78, how much do 5 kites cost? (a) ₹390 (b) ₹78 (c) ₹65 (d) ₹77
  34. 34.If 9 notebooks cost ₹180, how much do 2 notebooks cost? (a) ₹360 (b) ₹173 (c) ₹40 (d) ₹60
  35. 35.If 5 pens cost ₹65, how much do 6 pens cost? (a) ₹78 (b) ₹390 (c) ₹91 (d) ₹66
  36. 36.₹150 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹75 (c) ₹150 (d) ₹30
  37. 37.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹44 (c) ₹8 (d) ₹48
  38. 38.₹245 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹49 (b) ₹197 (c) ₹196 (d) ₹245
  39. 39.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹64 (d) ₹8
  40. 40.If 4 mangoes cost ₹68, how much do 7 mangoes cost? (a) ₹136 (b) ₹476 (c) ₹71 (d) ₹119

Answer key

  1. 12 days
  2. ₹32
  3. ₹92
  4. ₹35
  5. 33 days
  6. ₹280
  7. 2 days
  8. ₹15
  9. ₹30
  10. ₹117
  11. ₹54
  12. 35 days
  13. ₹216
  14. ₹36
  15. 21 days
  16. 16 days
  17. 5 days
  18. ₹72
  19. ₹30
  20. ₹32
  21. ₹30
  22. ₹216
  23. ₹24
  24. ₹51
  25. ₹120
  26. ₹162
  27. ₹54
  28. ₹33
  29. 25 days
  30. 7 days
  31. ₹150
  32. 20 days
  33. ₹65
  34. ₹40
  35. ₹78
  36. ₹120
  37. ₹48
  38. ₹196
  39. ₹64
  40. ₹119

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