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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 250 · 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.If 9 mangoes cost ₹153, how much do 7 mangoes cost? (a) ₹136 (b) ₹151 (c) ₹1071 (d) ₹119
  2. 2.If 3 mangoes cost ₹9, how much do 10 mangoes cost? (a) ₹16 (b) ₹30 (c) ₹90 (d) ₹33
  3. 3.If 3 notebooks cost ₹33, how much do 9 notebooks cost? (a) ₹297 (b) ₹99 (c) ₹110 (d) ₹39
  4. 4.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
  5. 5.If 8 notebooks cost ₹168, how much do 9 notebooks cost? (a) ₹1512 (b) ₹169 (c) ₹210 (d) ₹189
  6. 6.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 3 days (d) 2 days
  7. 7.If 5 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹120 (b) ₹32 (c) ₹24 (d) ₹38
  8. 8.If 6 kites cost ₹96, how much do 9 kites cost? (a) ₹160 (b) ₹99 (c) ₹144 (d) ₹864
  9. 9.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹20 (b) ₹16 (c) ₹25 (d) ₹60
  10. 10.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days
  11. 11.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 24 days (d) 12 days
  12. 12.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 18 days (d) 2 days
  13. 13.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 19 days (c) 11 days (d) 35 days
  14. 14.If 3 notebooks cost ₹54, how much do 6 notebooks cost? (a) ₹108 (b) ₹57 (c) ₹126 (d) ₹324
  15. 15.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 27 days (c) 11 days (d) 28 days
  16. 16.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days
  17. 17.If 4 kites cost ₹72, how much do 5 kites cost? (a) ₹90 (b) ₹73 (c) ₹360 (d) ₹108
  18. 18.If 5 mangoes cost ₹110, how much do 11 mangoes cost? (a) ₹242 (b) ₹116 (c) ₹264 (d) ₹1210
  19. 19.If 4 notebooks cost ₹80, how much do 2 notebooks cost? (a) ₹78 (b) ₹40 (c) ₹60 (d) ₹160
  20. 20.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 10 days (d) 12 days
  21. 21.If 4 pens cost ₹100, how much do 2 pens cost? (a) ₹98 (b) ₹200 (c) ₹50 (d) ₹75
  22. 22.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 6 days (d) 3 days
  23. 23.₹224 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹16 (b) ₹112 (c) ₹80 (d) ₹144
  24. 24.₹252 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹126 (d) ₹210
  25. 25.If 3 kites cost ₹24, how much do 4 kites cost? (a) ₹25 (b) ₹96 (c) ₹32 (d) ₹40
  26. 26.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 16 days (d) 15 days
  27. 27.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 17 days (d) 22 days
  28. 28.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 42 days (c) 43 days (d) 10 days
  29. 29.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 8 days (d) 7 days
  30. 30.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹128 (c) ₹160 (d) ₹32
  31. 31.If 7 mangoes cost ₹56, how much do 3 mangoes cost? (a) ₹52 (b) ₹168 (c) ₹32 (d) ₹24
  32. 32.If 9 mangoes cost ₹72, how much do 6 mangoes cost? (a) ₹69 (b) ₹56 (c) ₹432 (d) ₹48
  33. 33.If 3 notebooks cost ₹15, how much do 4 notebooks cost? (a) ₹60 (b) ₹25 (c) ₹20 (d) ₹16
  34. 34.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 2 days (d) 10 days
  35. 35.If 6 kites cost ₹66, how much do 5 kites cost? (a) ₹65 (b) ₹55 (c) ₹66 (d) ₹330
  36. 36.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹80 (b) ₹70 (c) ₹60 (d) ₹20
  37. 37.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
  38. 38.If 5 pens cost ₹55, how much do 6 pens cost? (a) ₹77 (b) ₹330 (c) ₹66 (d) ₹56
  39. 39.₹90 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹45 (b) ₹80 (c) ₹90 (d) ₹10
  40. 40.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹60 (c) ₹70 (d) ₹10

Answer key

  1. ₹119
  2. ₹30
  3. ₹99
  4. 3 days
  5. ₹189
  6. 3 days
  7. ₹24
  8. ₹144
  9. ₹20
  10. 7 days
  11. 24 days
  12. 2 days
  13. 35 days
  14. ₹108
  15. 27 days
  16. 45 days
  17. ₹90
  18. ₹242
  19. ₹40
  20. 12 days
  21. ₹50
  22. 3 days
  23. ₹144
  24. ₹210
  25. ₹32
  26. 15 days
  27. 21 days
  28. 42 days
  29. 7 days
  30. ₹160
  31. ₹24
  32. ₹48
  33. ₹20
  34. 18 days
  35. ₹55
  36. ₹80
  37. 27 days
  38. ₹66
  39. ₹80
  40. ₹60

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