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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 508 · 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 6 pens cost ₹54, how much do 4 pens cost? (a) ₹52 (b) ₹36 (c) ₹45 (d) ₹216
  2. 2.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹60 (b) ₹144 (c) ₹37 (d) ₹48
  3. 3.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 11 days
  4. 4.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 7 days (d) 25 days
  5. 5.If 7 pens cost ₹84, how much do 6 pens cost? (a) ₹504 (b) ₹72 (c) ₹84 (d) ₹83
  6. 6.₹528 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹308 (b) ₹44 (c) ₹220 (d) ₹264
  7. 7.If 7 kites cost ₹161, how much do 8 kites cost? (a) ₹162 (b) ₹1288 (c) ₹207 (d) ₹184
  8. 8.₹484 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹176 (b) ₹44 (c) ₹308 (d) ₹242
  9. 9.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 9 days (d) 2 days
  10. 10.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 6 days
  11. 11.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹17 (b) ₹136 (c) ₹153 (d) ₹137
  12. 12.₹209 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹133 (b) ₹19 (c) ₹76 (d) ₹152
  13. 13.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 22 days (d) 21 days
  14. 14.8 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 12 days (c) 11 days (d) 13 days
  15. 15.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 14 days (d) 4 days
  16. 16.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹99 (b) ₹18 (c) ₹108 (d) ₹90
  17. 17.If 8 pens cost ₹192, how much do 9 pens cost? (a) ₹216 (b) ₹193 (c) ₹240 (d) ₹1728
  18. 18.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 9 days (d) 8 days
  19. 19.₹245 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹196 (d) ₹147
  20. 20.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹135 (c) ₹15 (d) ₹120
  21. 21.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 9 days (d) 14 days
  22. 22.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 4 days (d) 9 days
  23. 23.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 9 days (c) 22 days (d) 13 days
  24. 24.If 9 notebooks cost ₹90, how much do 6 notebooks cost? (a) ₹60 (b) ₹87 (c) ₹70 (d) ₹540
  25. 25.If 9 notebooks cost ₹225, how much do 6 notebooks cost? (a) ₹222 (b) ₹175 (c) ₹1350 (d) ₹150
  26. 26.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹35 (b) ₹210 (c) ₹175 (d) ₹245
  27. 27.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹55 (b) ₹22 (c) ₹11 (d) ₹66
  28. 28.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹18 (b) ₹54 (c) ₹90 (d) ₹108
  29. 29.If 4 pens cost ₹88, how much do 6 pens cost? (a) ₹90 (b) ₹154 (c) ₹528 (d) ₹132
  30. 30.₹252 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹105 (b) ₹21 (c) ₹126 (d) ₹147
  31. 31.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹45 (b) ₹36 (c) ₹54 (d) ₹9
  32. 32.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹68 (b) ₹187 (c) ₹34 (d) ₹306
  33. 33.If 7 mangoes cost ₹77, how much do 2 mangoes cost? (a) ₹33 (b) ₹154 (c) ₹22 (d) ₹72
  34. 34.If 2 pens cost ₹36, how much do 3 pens cost? (a) ₹72 (b) ₹108 (c) ₹54 (d) ₹37
  35. 35.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 11 days (d) 5 days
  36. 36.If 7 notebooks cost ₹56, how much do 9 notebooks cost? (a) ₹504 (b) ₹72 (c) ₹58 (d) ₹80
  37. 37.If 5 kites cost ₹85, how much do 8 kites cost? (a) ₹136 (b) ₹680 (c) ₹88 (d) ₹153
  38. 38.If 2 notebooks cost ₹48, how much do 9 notebooks cost? (a) ₹432 (b) ₹216 (c) ₹240 (d) ₹55
  39. 39.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 17 days (d) 16 days
  40. 40.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 27 days (c) 15 days (d) 3 days

Answer key

  1. ₹36
  2. ₹48
  3. 7 days
  4. 25 days
  5. ₹72
  6. ₹308
  7. ₹184
  8. ₹308
  9. 8 days
  10. 7 days
  11. ₹136
  12. ₹133
  13. 21 days
  14. 12 days
  15. 14 days
  16. ₹108
  17. ₹216
  18. 4 days
  19. ₹147
  20. ₹120
  21. 16 days
  22. 9 days
  23. 22 days
  24. ₹60
  25. ₹150
  26. ₹245
  27. ₹55
  28. ₹90
  29. ₹132
  30. ₹147
  31. ₹45
  32. ₹306
  33. ₹22
  34. ₹54
  35. 5 days
  36. ₹72
  37. ₹136
  38. ₹216
  39. 16 days
  40. 3 days

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