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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 192 · 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 4 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹72 (b) ₹94 (c) ₹192 (d) ₹48
  2. 2.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹7 (b) ₹14 (c) ₹15 (d) ₹21
  3. 3.If 9 pens cost ₹27, how much do 5 pens cost? (a) ₹135 (b) ₹18 (c) ₹15 (d) ₹23
  4. 4.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 9 days
  5. 5.If 3 kites cost ₹42, how much do 9 kites cost? (a) ₹140 (b) ₹126 (c) ₹378 (d) ₹48
  6. 6.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 5 days (d) 13 days
  7. 7.If 4 notebooks cost ₹80, how much do 5 notebooks cost? (a) ₹400 (b) ₹100 (c) ₹81 (d) ₹120
  8. 8.₹117 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹72 (b) ₹45 (c) ₹81 (d) ₹9
  9. 9.If 4 pens cost ₹20, how much do 5 pens cost? (a) ₹21 (b) ₹100 (c) ₹30 (d) ₹25
  10. 10.₹344 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹43 (b) ₹344 (c) ₹301 (d) ₹172
  11. 11.If 2 pens cost ₹8, how much do 7 pens cost? (a) ₹56 (b) ₹13 (c) ₹28 (d) ₹32
  12. 12.If 7 kites cost ₹154, how much do 12 kites cost? (a) ₹286 (b) ₹1848 (c) ₹264 (d) ₹159
  13. 13.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 12 days (d) 8 days
  14. 14.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹208 (b) ₹104 (c) ₹26 (d) ₹182
  15. 15.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹230 (b) ₹46 (c) ₹184 (d) ₹115
  16. 16.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 14 days (d) 15 days
  17. 17.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 3 days (d) 2 days
  18. 18.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹15 (b) ₹12 (c) ₹36 (d) ₹10
  19. 19.If 3 kites cost ₹42, how much do 2 kites cost? (a) ₹42 (b) ₹41 (c) ₹84 (d) ₹28
  20. 20.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹204 (d) ₹187
  21. 21.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 11 days (d) 19 days
  22. 22.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 10 days (d) 11 days
  23. 23.If 2 notebooks cost ₹34, how much do 12 notebooks cost? (a) ₹221 (b) ₹204 (c) ₹44 (d) ₹408
  24. 24.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹26 (b) ₹78 (c) ₹52 (d) ₹65
  25. 25.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 10 days (d) 18 days
  26. 26.₹288 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹288 (b) ₹144 (c) ₹36 (d) ₹252
  27. 27.If 8 notebooks cost ₹56, how much do 11 notebooks cost? (a) ₹84 (b) ₹77 (c) ₹616 (d) ₹59
  28. 28.If 9 mangoes cost ₹126, how much do 7 mangoes cost? (a) ₹124 (b) ₹112 (c) ₹882 (d) ₹98
  29. 29.If 2 mangoes cost ₹8, how much do 3 mangoes cost? (a) ₹24 (b) ₹12 (c) ₹9 (d) ₹16
  30. 30.If 5 notebooks cost ₹80, how much do 10 notebooks cost? (a) ₹176 (b) ₹160 (c) ₹85 (d) ₹800
  31. 31.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹279 (d) ₹217
  32. 32.₹104 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹65 (b) ₹39 (c) ₹13 (d) ₹52
  33. 33.If 6 pens cost ₹66, how much do 5 pens cost? (a) ₹65 (b) ₹66 (c) ₹55 (d) ₹330
  34. 34.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 53 days (c) 7 days (d) 19 days
  35. 35.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 44 days (c) 17 days (d) 45 days
  36. 36.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 28 days (d) 20 days
  37. 37.If 7 notebooks cost ₹105, how much do 8 notebooks cost? (a) ₹106 (b) ₹135 (c) ₹840 (d) ₹120
  38. 38.If 6 notebooks cost ₹96, how much do 2 notebooks cost? (a) ₹92 (b) ₹32 (c) ₹48 (d) ₹192
  39. 39.If 5 kites cost ₹110, how much do 4 kites cost? (a) ₹110 (b) ₹88 (c) ₹109 (d) ₹440
  40. 40.If 9 mangoes cost ₹153, how much do 10 mangoes cost? (a) ₹187 (b) ₹1530 (c) ₹170 (d) ₹154

Answer key

  1. ₹48
  2. ₹14
  3. ₹15
  4. 9 days
  5. ₹126
  6. 27 days
  7. ₹100
  8. ₹72
  9. ₹25
  10. ₹301
  11. ₹28
  12. ₹264
  13. 12 days
  14. ₹182
  15. ₹184
  16. 14 days
  17. 3 days
  18. ₹12
  19. ₹28
  20. ₹204
  21. 27 days
  22. 10 days
  23. ₹204
  24. ₹78
  25. 6 days
  26. ₹252
  27. ₹77
  28. ₹98
  29. ₹12
  30. ₹160
  31. ₹279
  32. ₹65
  33. ₹55
  34. 52 days
  35. 44 days
  36. 7 days
  37. ₹120
  38. ₹32
  39. ₹88
  40. ₹170

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