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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 332 · 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 9 kites cost ₹171, how much do 3 kites cost? (a) ₹165 (b) ₹57 (c) ₹76 (d) ₹513
  2. 2.If 4 notebooks cost ₹64, how much do 5 notebooks cost? (a) ₹65 (b) ₹320 (c) ₹80 (d) ₹96
  3. 3.If 5 mangoes cost ₹125, how much do 8 mangoes cost? (a) ₹200 (b) ₹128 (c) ₹225 (d) ₹1000
  4. 4.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 16 days (d) 5 days
  5. 5.If 8 kites cost ₹184, how much do 3 kites cost? (a) ₹179 (b) ₹552 (c) ₹92 (d) ₹69
  6. 6.₹50 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹50 (b) ₹25 (c) ₹40 (d) ₹10
  7. 7.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹200 (b) ₹55 (c) ₹50 (d) ₹26
  8. 8.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹32 (b) ₹8 (c) ₹52 (d) ₹72
  9. 9.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 13 days (d) 18 days
  10. 10.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 14 days (c) 5 days (d) 7 days
  11. 11.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹11 (b) ₹99 (c) ₹77 (d) ₹55
  12. 12.If 3 pens cost ₹72, how much do 12 pens cost? (a) ₹312 (b) ₹81 (c) ₹864 (d) ₹288
  13. 13.₹108 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹12 (b) ₹54 (c) ₹108 (d) ₹96
  14. 14.If 9 mangoes cost ₹27, how much do 12 mangoes cost? (a) ₹36 (b) ₹324 (c) ₹39 (d) ₹30
  15. 15.₹320 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹320 (b) ₹160 (c) ₹32 (d) ₹288
  16. 16.If 9 kites cost ₹216, how much do 6 kites cost? (a) ₹1296 (b) ₹213 (c) ₹168 (d) ₹144
  17. 17.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 43 days (c) 20 days (d) 42 days
  18. 18.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 4 days (d) 8 days
  19. 19.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 5 days (d) 13 days
  20. 20.If 9 pens cost ₹126, how much do 11 pens cost? (a) ₹154 (b) ₹168 (c) ₹128 (d) ₹1386
  21. 21.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 1 day (d) 16 days
  22. 22.If 5 kites cost ₹15, how much do 12 kites cost? (a) ₹180 (b) ₹39 (c) ₹36 (d) ₹22
  23. 23.If 3 pens cost ₹27, how much do 11 pens cost? (a) ₹35 (b) ₹108 (c) ₹297 (d) ₹99
  24. 24.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 56 days (d) 20 days
  25. 25.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹68 (b) ₹51 (c) ₹85 (d) ₹17
  26. 26.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹333 (b) ₹111 (c) ₹37 (d) ₹296
  27. 27.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 3 days (d) 13 days
  28. 28.₹105 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹42 (b) ₹63 (c) ₹84 (d) ₹21
  29. 29.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹115 (b) ₹92 (c) ₹23 (d) ₹69
  30. 30.6 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 4 days (d) 9 days
  31. 31.If 8 mangoes cost ₹40, how much do 11 mangoes cost? (a) ₹440 (b) ₹43 (c) ₹55 (d) ₹60
  32. 32.If 8 notebooks cost ₹104, how much do 5 notebooks cost? (a) ₹101 (b) ₹520 (c) ₹78 (d) ₹65
  33. 33.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 13 days (c) 26 days (d) 28 days
  34. 34.₹423 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹377 (b) ₹376 (c) ₹47 (d) ₹423
  35. 35.If 4 notebooks cost ₹100, how much do 2 notebooks cost? (a) ₹75 (b) ₹200 (c) ₹98 (d) ₹50
  36. 36.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹175 (b) ₹25 (c) ₹125 (d) ₹150
  37. 37.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 20 days (d) 5 days
  38. 38.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹188 (b) ₹47 (c) ₹94 (d) ₹141
  39. 39.If 7 kites cost ₹161, how much do 11 kites cost? (a) ₹276 (b) ₹1771 (c) ₹253 (d) ₹165
  40. 40.If 7 notebooks cost ₹42, how much do 8 notebooks cost? (a) ₹54 (b) ₹336 (c) ₹43 (d) ₹48

Answer key

  1. ₹57
  2. ₹80
  3. ₹200
  4. 4 days
  5. ₹69
  6. ₹40
  7. ₹50
  8. ₹72
  9. 18 days
  10. 6 days
  11. ₹99
  12. ₹288
  13. ₹96
  14. ₹36
  15. ₹288
  16. ₹144
  17. 42 days
  18. 10 days
  19. 5 days
  20. ₹154
  21. 16 days
  22. ₹36
  23. ₹99
  24. 56 days
  25. ₹68
  26. ₹296
  27. 12 days
  28. ₹63
  29. ₹115
  30. 9 days
  31. ₹55
  32. ₹65
  33. 27 days
  34. ₹376
  35. ₹50
  36. ₹150
  37. 5 days
  38. ₹141
  39. ₹253
  40. ₹48

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