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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 182 · 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 7 notebooks cost ₹49, how much do 8 notebooks cost? (a) ₹63 (b) ₹392 (c) ₹50 (d) ₹56
  2. 2.If 5 notebooks cost ₹40, how much do 11 notebooks cost? (a) ₹96 (b) ₹440 (c) ₹46 (d) ₹88
  3. 3.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 15 days
  4. 4.If 6 notebooks cost ₹144, how much do 9 notebooks cost? (a) ₹240 (b) ₹1296 (c) ₹216 (d) ₹147
  5. 5.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 28 days (c) 7 days (d) 8 days
  6. 6.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 16 days (d) 15 days
  7. 7.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹201 (b) ₹200 (c) ₹225 (d) ₹25
  8. 8.If 9 pens cost ₹72, how much do 5 pens cost? (a) ₹68 (b) ₹40 (c) ₹48 (d) ₹360
  9. 9.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 2 days
  10. 10.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 6 days (d) 7 days
  11. 11.If 7 kites cost ₹168, how much do 5 kites cost? (a) ₹166 (b) ₹840 (c) ₹144 (d) ₹120
  12. 12.If 6 mangoes cost ₹114, how much do 9 mangoes cost? (a) ₹171 (b) ₹117 (c) ₹190 (d) ₹1026
  13. 13.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 4 days (d) 11 days
  14. 14.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹23 (b) ₹92 (c) ₹230 (d) ₹207
  15. 15.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹180 (c) ₹165 (d) ₹30
  16. 16.If 3 kites cost ₹21, how much do 10 kites cost? (a) ₹77 (b) ₹28 (c) ₹210 (d) ₹70
  17. 17.If 5 kites cost ₹45, how much do 8 kites cost? (a) ₹48 (b) ₹72 (c) ₹360 (d) ₹81
  18. 18.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹148 (b) ₹222 (c) ₹185 (d) ₹37
  19. 19.If 8 kites cost ₹120, how much do 6 kites cost? (a) ₹90 (b) ₹118 (c) ₹105 (d) ₹720
  20. 20.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹17 (d) ₹51
  21. 21.If 2 notebooks cost ₹18, how much do 7 notebooks cost? (a) ₹126 (b) ₹72 (c) ₹63 (d) ₹23
  22. 22.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 11 days (d) 21 days
  23. 23.If 6 notebooks cost ₹30, how much do 12 notebooks cost? (a) ₹60 (b) ₹360 (c) ₹65 (d) ₹36
  24. 24.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 6 days (d) 5 days
  25. 25.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹432 (b) ₹48 (c) ₹336 (d) ₹240
  26. 26.If 4 pens cost ₹80, how much do 12 pens cost? (a) ₹240 (b) ₹88 (c) ₹960 (d) ₹260
  27. 27.₹54 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹27 (c) ₹9 (d) ₹54
  28. 28.₹506 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹253 (b) ₹276 (c) ₹46 (d) ₹230
  29. 29.If 4 pens cost ₹72, how much do 6 pens cost? (a) ₹126 (b) ₹74 (c) ₹432 (d) ₹108
  30. 30.If 8 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹36 (b) ₹192 (c) ₹90 (d) ₹24
  31. 31.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹20 (c) ₹5 (d) ₹40
  32. 32.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹13 (d) ₹91
  33. 33.If 3 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹96 (b) ₹84 (c) ₹40 (d) ₹252
  34. 34.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 5 days (d) 45 days
  35. 35.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 7 days (d) 15 days
  36. 36.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 1 day
  37. 37.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
  38. 38.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 15 days (d) 14 days
  39. 39.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 13 days (d) 9 days
  40. 40.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days

Answer key

  1. ₹56
  2. ₹88
  3. 7 days
  4. ₹216
  5. 7 days
  6. 15 days
  7. ₹200
  8. ₹40
  9. 8 days
  10. 8 days
  11. ₹120
  12. ₹171
  13. 16 days
  14. ₹207
  15. ₹180
  16. ₹70
  17. ₹72
  18. ₹185
  19. ₹90
  20. ₹51
  21. ₹63
  22. 21 days
  23. ₹60
  24. 5 days
  25. ₹432
  26. ₹240
  27. ₹45
  28. ₹276
  29. ₹108
  30. ₹24
  31. ₹35
  32. ₹78
  33. ₹84
  34. 45 days
  35. 15 days
  36. 2 days
  37. 7 days
  38. 14 days
  39. 25 days
  40. 3 days

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