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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 626 · 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 5 notebooks cost ₹110, how much do 3 notebooks cost? (a) ₹330 (b) ₹88 (c) ₹108 (d) ₹66
  2. 2.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 8 days (c) 36 days (d) 16 days
  3. 3.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 10 days (c) 2 days (d) 18 days
  4. 4.If 4 mangoes cost ₹64, how much do 9 mangoes cost? (a) ₹160 (b) ₹69 (c) ₹144 (d) ₹576
  5. 5.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹111 (b) ₹148 (c) ₹74 (d) ₹37
  6. 6.If 9 mangoes cost ₹54, how much do 8 mangoes cost? (a) ₹54 (b) ₹53 (c) ₹432 (d) ₹48
  7. 7.If 6 mangoes cost ₹60, how much do 9 mangoes cost? (a) ₹100 (b) ₹63 (c) ₹90 (d) ₹540
  8. 8.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 20 days (c) 5 days (d) 14 days
  9. 9.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹189 (d) ₹135
  10. 10.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹216 (b) ₹72 (c) ₹90 (d) ₹55
  11. 11.If 4 pens cost ₹16, how much do 11 pens cost? (a) ₹44 (b) ₹48 (c) ₹176 (d) ₹23
  12. 12.If 4 kites cost ₹52, how much do 12 kites cost? (a) ₹156 (b) ₹624 (c) ₹60 (d) ₹169
  13. 13.₹432 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹180 (b) ₹252 (c) ₹36 (d) ₹216
  14. 14.If 9 mangoes cost ₹135, how much do 10 mangoes cost? (a) ₹150 (b) ₹165 (c) ₹136 (d) ₹1350
  15. 15.If 9 kites cost ₹135, how much do 3 kites cost? (a) ₹60 (b) ₹45 (c) ₹405 (d) ₹129
  16. 16.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 7 days (d) 1 day
  17. 17.If 3 pens cost ₹15, how much do 11 pens cost? (a) ₹60 (b) ₹23 (c) ₹55 (d) ₹165
  18. 18.If 3 pens cost ₹72, how much do 8 pens cost? (a) ₹576 (b) ₹192 (c) ₹77 (d) ₹216
  19. 19.If 3 notebooks cost ₹66, how much do 8 notebooks cost? (a) ₹71 (b) ₹198 (c) ₹176 (d) ₹528
  20. 20.₹88 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹32 (d) ₹44
  21. 21.If 7 pens cost ₹77, how much do 3 pens cost? (a) ₹73 (b) ₹231 (c) ₹33 (d) ₹44
  22. 22.If 3 notebooks cost ₹12, how much do 10 notebooks cost? (a) ₹19 (b) ₹44 (c) ₹40 (d) ₹120
  23. 23.If 2 pens cost ₹20, how much do 9 pens cost? (a) ₹90 (b) ₹100 (c) ₹180 (d) ₹27
  24. 24.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 2 days
  25. 25.If 3 pens cost ₹66, how much do 10 pens cost? (a) ₹660 (b) ₹73 (c) ₹220 (d) ₹242
  26. 26.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹209 (b) ₹228 (c) ₹190 (d) ₹38
  27. 27.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹105 (b) ₹15 (c) ₹30 (d) ₹120
  28. 28.If 3 pens cost ₹45, how much do 5 pens cost? (a) ₹47 (b) ₹90 (c) ₹225 (d) ₹75
  29. 29.If 7 pens cost ₹168, how much do 10 pens cost? (a) ₹1680 (b) ₹240 (c) ₹171 (d) ₹264
  30. 30.If 8 pens cost ₹56, how much do 10 pens cost? (a) ₹560 (b) ₹77 (c) ₹70 (d) ₹58
  31. 31.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 21 days (c) 20 days (d) 16 days
  32. 32.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 18 days (d) 8 days
  33. 33.If 4 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹40 (b) ₹288 (c) ₹72 (d) ₹81
  34. 34.If 7 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹51 (b) ₹24 (c) ₹16 (d) ₹112
  35. 35.If 2 pens cost ₹24, how much do 12 pens cost? (a) ₹144 (b) ₹288 (c) ₹34 (d) ₹156
  36. 36.If 7 mangoes cost ₹35, how much do 8 mangoes cost? (a) ₹280 (b) ₹45 (c) ₹40 (d) ₹36
  37. 37.If 8 notebooks cost ₹192, how much do 4 notebooks cost? (a) ₹188 (b) ₹96 (c) ₹768 (d) ₹120
  38. 38.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 7 days
  39. 39.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 16 days (c) 4 days (d) 5 days
  40. 40.If 5 mangoes cost ₹125, how much do 6 mangoes cost? (a) ₹175 (b) ₹126 (c) ₹150 (d) ₹750

Answer key

  1. ₹66
  2. 36 days
  3. 18 days
  4. ₹144
  5. ₹111
  6. ₹48
  7. ₹90
  8. 5 days
  9. ₹162
  10. ₹72
  11. ₹44
  12. ₹156
  13. ₹252
  14. ₹150
  15. ₹45
  16. 3 days
  17. ₹55
  18. ₹192
  19. ₹176
  20. ₹56
  21. ₹33
  22. ₹40
  23. ₹90
  24. 8 days
  25. ₹220
  26. ₹228
  27. ₹105
  28. ₹75
  29. ₹240
  30. ₹70
  31. 20 days
  32. 8 days
  33. ₹72
  34. ₹16
  35. ₹144
  36. ₹40
  37. ₹96
  38. 6 days
  39. 4 days
  40. ₹150

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