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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 152 · 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.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹198 (d) ₹216
  2. 2.If 2 pens cost ₹40, how much do 10 pens cost? (a) ₹400 (b) ₹48 (c) ₹200 (d) ₹220
  3. 3.₹253 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹46 (d) ₹230
  4. 4.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 19 days (d) 28 days
  5. 5.If 2 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹160 (b) ₹144 (c) ₹288 (d) ₹39
  6. 6.₹152 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹95 (b) ₹19 (c) ₹57 (d) ₹76
  7. 7.If 3 pens cost ₹54, how much do 4 pens cost? (a) ₹216 (b) ₹72 (c) ₹55 (d) ₹90
  8. 8.If 7 kites cost ₹168, how much do 3 kites cost? (a) ₹164 (b) ₹72 (c) ₹96 (d) ₹504
  9. 9.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 8 days (d) 7 days
  10. 10.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 23 days (c) 15 days (d) 7 days
  11. 11.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 5 days (d) 4 days
  12. 12.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹25 (b) ₹16 (c) ₹20 (d) ₹60
  13. 13.If 3 pens cost ₹45, how much do 6 pens cost? (a) ₹90 (b) ₹270 (c) ₹105 (d) ₹48
  14. 14.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹15 (b) ₹13 (c) ₹18 (d) ₹60
  15. 15.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹160 (b) ₹40 (c) ₹360 (d) ₹260
  16. 16.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹36 (d) ₹16
  17. 17.If 8 mangoes cost ₹192, how much do 2 mangoes cost? (a) ₹186 (b) ₹384 (c) ₹72 (d) ₹48
  18. 18.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹99 (c) ₹162 (d) ₹36
  19. 19.If 2 notebooks cost ₹14, how much do 10 notebooks cost? (a) ₹140 (b) ₹77 (c) ₹70 (d) ₹22
  20. 20.₹430 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹215 (d) ₹129
  21. 21.₹279 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹249 (b) ₹248 (c) ₹279 (d) ₹31
  22. 22.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 16 days (d) 9 days
  23. 23.If 4 kites cost ₹96, how much do 12 kites cost? (a) ₹288 (b) ₹312 (c) ₹1152 (d) ₹104
  24. 24.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹150 (b) ₹250 (c) ₹50 (d) ₹300
  25. 25.If 9 notebooks cost ₹90, how much do 5 notebooks cost? (a) ₹50 (b) ₹60 (c) ₹86 (d) ₹450
  26. 26.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 11 days
  27. 27.If 8 pens cost ₹152, how much do 6 pens cost? (a) ₹114 (b) ₹133 (c) ₹150 (d) ₹912
  28. 28.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 29 days (d) 28 days
  29. 29.If 7 pens cost ₹63, how much do 10 pens cost? (a) ₹90 (b) ₹66 (c) ₹99 (d) ₹630
  30. 30.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 40 days (c) 19 days (d) 39 days
  31. 31.If 6 pens cost ₹24, how much do 12 pens cost? (a) ₹52 (b) ₹30 (c) ₹48 (d) ₹288
  32. 32.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 8 days (d) 13 days
  33. 33.₹90 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹60 (b) ₹30 (c) ₹45 (d) ₹90
  34. 34.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 18 days (c) 10 days (d) 19 days
  35. 35.If 5 mangoes cost ₹95, how much do 2 mangoes cost? (a) ₹57 (b) ₹38 (c) ₹92 (d) ₹190
  36. 36.If 4 mangoes cost ₹12, how much do 6 mangoes cost? (a) ₹18 (b) ₹21 (c) ₹14 (d) ₹72
  37. 37.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹128 (b) ₹16 (c) ₹58 (d) ₹24
  38. 38.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
  39. 39.If 2 pens cost ₹38, how much do 4 pens cost? (a) ₹152 (b) ₹76 (c) ₹40 (d) ₹95
  40. 40.₹611 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹47 (b) ₹470 (c) ₹423 (d) ₹188

Answer key

  1. ₹216
  2. ₹200
  3. ₹207
  4. 27 days
  5. ₹144
  6. ₹95
  7. ₹72
  8. ₹72
  9. 7 days
  10. 22 days
  11. 5 days
  12. ₹20
  13. ₹90
  14. ₹15
  15. ₹360
  16. ₹56
  17. ₹48
  18. ₹162
  19. ₹70
  20. ₹301
  21. ₹248
  22. 16 days
  23. ₹288
  24. ₹250
  25. ₹50
  26. 3 days
  27. ₹114
  28. 28 days
  29. ₹90
  30. 39 days
  31. ₹48
  32. 9 days
  33. ₹60
  34. 18 days
  35. ₹38
  36. ₹18
  37. ₹16
  38. 8 days
  39. ₹76
  40. ₹423

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