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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 716 · 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. 1.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 28 days (d) 12 days
  2. 2.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹104 (d) ₹26
  3. 3.If 2 notebooks cost ₹44, how much do 5 notebooks cost? (a) ₹220 (b) ₹110 (c) ₹132 (d) ₹47
  4. 4.7 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) 7 days (d) 8 days
  5. 5.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 9 days (d) 2 days
  6. 6.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹80 (d) ₹16
  7. 7.₹418 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹209 (b) ₹76 (c) ₹342 (d) ₹38
  8. 8.If 4 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹60 (b) ₹42 (c) ₹240 (d) ₹70
  9. 9.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 13 days (d) 3 days
  10. 10.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹270 (b) ₹243 (c) ₹108 (d) ₹27
  11. 11.9 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) 21 days (d) 45 days
  12. 12.If 9 kites cost ₹90, how much do 10 kites cost? (a) ₹100 (b) ₹110 (c) ₹91 (d) ₹900
  13. 13.If 8 pens cost ₹168, how much do 7 pens cost? (a) ₹1176 (b) ₹167 (c) ₹147 (d) ₹168
  14. 14.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹48 (d) ₹32
  15. 15.If 4 pens cost ₹16, how much do 5 pens cost? (a) ₹24 (b) ₹20 (c) ₹80 (d) ₹17
  16. 16.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹225 (b) ₹125 (c) ₹200 (d) ₹25
  17. 17.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 8 days (d) 9 days
  18. 18.If 6 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹864 (b) ₹144 (c) ₹156 (d) ₹78
  19. 19.If 3 kites cost ₹54, how much do 2 kites cost? (a) ₹108 (b) ₹53 (c) ₹36 (d) ₹54
  20. 20.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 14 days (d) 15 days
  21. 21.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹21 (b) ₹42 (c) ₹210 (d) ₹189
  22. 22.If 2 pens cost ₹50, how much do 4 pens cost? (a) ₹100 (b) ₹52 (c) ₹125 (d) ₹200
  23. 23.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 11 days (d) 14 days
  24. 24.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 8 days (d) 9 days
  25. 25.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 13 days (d) 11 days
  26. 26.₹506 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹184 (b) ₹322 (c) ₹253 (d) ₹46
  27. 27.If 7 pens cost ₹77, how much do 5 pens cost? (a) ₹66 (b) ₹55 (c) ₹75 (d) ₹385
  28. 28.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 64 days (d) 63 days
  29. 29.If 2 notebooks cost ₹14, how much do 12 notebooks cost? (a) ₹24 (b) ₹168 (c) ₹91 (d) ₹84
  30. 30.If 9 kites cost ₹180, how much do 4 kites cost? (a) ₹100 (b) ₹720 (c) ₹175 (d) ₹80
  31. 31.₹90 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹75 (d) ₹90
  32. 32.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹245 (b) ₹35 (c) ₹210 (d) ₹211
  33. 33.If 4 notebooks cost ₹36, how much do 5 notebooks cost? (a) ₹37 (b) ₹45 (c) ₹54 (d) ₹180
  34. 34.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 15 days (d) 11 days
  35. 35.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 24 days (c) 12 days (d) 25 days
  36. 36.If 9 notebooks cost ₹54, how much do 6 notebooks cost? (a) ₹324 (b) ₹36 (c) ₹42 (d) ₹51
  37. 37.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 16 days (d) 15 days
  38. 38.If 2 kites cost ₹46, how much do 10 kites cost? (a) ₹253 (b) ₹54 (c) ₹460 (d) ₹230
  39. 39.₹152 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹133 (b) ₹76 (c) ₹19 (d) ₹152
  40. 40.If 3 kites cost ₹51, how much do 4 kites cost? (a) ₹52 (b) ₹204 (c) ₹85 (d) ₹68

Answer key

  1. 28 days
  2. ₹91
  3. ₹110
  4. 7 days
  5. 4 days
  6. ₹80
  7. ₹342
  8. ₹60
  9. 12 days
  10. ₹243
  11. 45 days
  12. ₹100
  13. ₹147
  14. ₹32
  15. ₹20
  16. ₹200
  17. 9 days
  18. ₹144
  19. ₹36
  20. 14 days
  21. ₹189
  22. ₹100
  23. 14 days
  24. 8 days
  25. 12 days
  26. ₹322
  27. ₹55
  28. 63 days
  29. ₹84
  30. ₹80
  31. ₹75
  32. ₹210
  33. ₹45
  34. 15 days
  35. 24 days
  36. ₹36
  37. 9 days
  38. ₹230
  39. ₹133
  40. ₹68

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