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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 142 · 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. 1.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 36 days (d) 35 days
  2. 2.If 2 kites cost ₹30, how much do 8 kites cost? (a) ₹135 (b) ₹36 (c) ₹240 (d) ₹120
  3. 3.If 4 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹120 (b) ₹40 (c) ₹39 (d) ₹30
  4. 4.If 4 kites cost ₹76, how much do 2 kites cost? (a) ₹152 (b) ₹74 (c) ₹57 (d) ₹38
  5. 5.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹24 (c) ₹72 (d) ₹120
  6. 6.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 23 days (d) 22 days
  7. 7.₹432 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹432 (c) ₹384 (d) ₹48
  8. 8.If 7 pens cost ₹105, how much do 6 pens cost? (a) ₹630 (b) ₹105 (c) ₹104 (d) ₹90
  9. 9.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 4 days (d) 3 days
  10. 10.₹343 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹196 (d) ₹245
  11. 11.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹47 (b) ₹282 (c) ₹235 (d) ₹329
  12. 12.₹114 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹57 (b) ₹114 (c) ₹95 (d) ₹19
  13. 13.₹360 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹40 (b) ₹80 (c) ₹180 (d) ₹280
  14. 14.If 4 kites cost ₹36, how much do 8 kites cost? (a) ₹288 (b) ₹40 (c) ₹81 (d) ₹72
  15. 15.If 7 mangoes cost ₹35, how much do 6 mangoes cost? (a) ₹34 (b) ₹210 (c) ₹35 (d) ₹30
  16. 16.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹16 (c) ₹72 (d) ₹128
  17. 17.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 16 days (d) 9 days
  18. 18.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹200 (b) ₹25 (c) ₹175 (d) ₹50
  19. 19.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 21 days (d) 22 days
  20. 20.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 5 days (d) 7 days
  21. 21.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹22 (b) ₹23 (c) ₹33 (d) ₹11
  22. 22.If 8 mangoes cost ₹24, how much do 12 mangoes cost? (a) ₹39 (b) ₹36 (c) ₹28 (d) ₹288
  23. 23.If 2 pens cost ₹28, how much do 9 pens cost? (a) ₹252 (b) ₹35 (c) ₹140 (d) ₹126
  24. 24.If 7 pens cost ₹42, how much do 2 pens cost? (a) ₹37 (b) ₹12 (c) ₹84 (d) ₹18
  25. 25.If 3 pens cost ₹57, how much do 6 pens cost? (a) ₹342 (b) ₹133 (c) ₹60 (d) ₹114
  26. 26.If 7 notebooks cost ₹56, how much do 2 notebooks cost? (a) ₹51 (b) ₹112 (c) ₹24 (d) ₹16
  27. 27.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 25 days (c) 12 days (d) 24 days
  28. 28.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 8 days
  29. 29.If 6 notebooks cost ₹144, how much do 12 notebooks cost? (a) ₹150 (b) ₹312 (c) ₹288 (d) ₹1728
  30. 30.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹110 (b) ₹120 (c) ₹20 (d) ₹100
  31. 31.If 7 kites cost ₹161, how much do 10 kites cost? (a) ₹164 (b) ₹253 (c) ₹1610 (d) ₹230
  32. 32.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹344 (b) ₹301 (c) ₹43 (d) ₹86
  33. 33.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 1 day (d) 29 days
  34. 34.If 2 kites cost ₹34, how much do 7 kites cost? (a) ₹238 (b) ₹39 (c) ₹136 (d) ₹119
  35. 35.If 5 pens cost ₹45, how much do 10 pens cost? (a) ₹99 (b) ₹50 (c) ₹90 (d) ₹450
  36. 36.₹171 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹76 (b) ₹114 (c) ₹19 (d) ₹95
  37. 37.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 17 days (d) 1 day
  38. 38.If 8 pens cost ₹24, how much do 4 pens cost? (a) ₹12 (b) ₹20 (c) ₹96 (d) ₹15
  39. 39.If 6 mangoes cost ₹48, how much do 2 mangoes cost? (a) ₹16 (b) ₹24 (c) ₹96 (d) ₹44
  40. 40.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹240 (b) ₹48 (c) ₹288 (d) ₹264

Answer key

  1. 35 days
  2. ₹120
  3. ₹30
  4. ₹38
  5. ₹120
  6. 22 days
  7. ₹384
  8. ₹90
  9. 3 days
  10. ₹196
  11. ₹282
  12. ₹95
  13. ₹280
  14. ₹72
  15. ₹30
  16. ₹128
  17. 9 days
  18. ₹175
  19. 21 days
  20. 6 days
  21. ₹22
  22. ₹36
  23. ₹126
  24. ₹12
  25. ₹114
  26. ₹16
  27. 24 days
  28. 7 days
  29. ₹288
  30. ₹120
  31. ₹230
  32. ₹301
  33. 28 days
  34. ₹119
  35. ₹90
  36. ₹95
  37. 16 days
  38. ₹12
  39. ₹16
  40. ₹288

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