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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 942 · 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. 1.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 3 days (d) 4 days
  2. 2.If 3 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹200 (b) ₹600 (c) ₹67 (d) ₹220
  3. 3.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹15 (c) ₹25 (d) ₹5
  4. 4.If 2 mangoes cost ₹14, how much do 10 mangoes cost? (a) ₹22 (b) ₹70 (c) ₹77 (d) ₹140
  5. 5.₹84 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹21 (d) ₹63
  6. 6.₹112 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹42 (b) ₹56 (c) ₹14 (d) ₹70
  7. 7.If 9 pens cost ₹36, how much do 3 pens cost? (a) ₹12 (b) ₹108 (c) ₹16 (d) ₹30
  8. 8.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 18 days (d) 11 days
  9. 9.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹28 (c) ₹8 (d) ₹32
  10. 10.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 7 days (d) 6 days
  11. 11.If 8 pens cost ₹192, how much do 2 pens cost? (a) ₹186 (b) ₹48 (c) ₹72 (d) ₹384
  12. 12.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹15 (b) ₹25 (c) ₹5 (d) ₹20
  13. 13.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹169 (c) ₹104 (d) ₹26
  14. 14.If 3 notebooks cost ₹21, how much do 12 notebooks cost? (a) ₹91 (b) ₹84 (c) ₹252 (d) ₹30
  15. 15.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹240 (b) ₹49 (c) ₹60 (d) ₹72
  16. 16.If 3 pens cost ₹9, how much do 12 pens cost? (a) ₹108 (b) ₹36 (c) ₹18 (d) ₹39
  17. 17.4 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
  18. 18.₹217 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹124 (d) ₹155
  19. 19.If 4 pens cost ₹92, how much do 10 pens cost? (a) ₹253 (b) ₹920 (c) ₹230 (d) ₹98
  20. 20.₹407 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹259 (b) ₹37 (c) ₹185 (d) ₹222
  21. 21.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹225 (c) ₹200 (d) ₹25
  22. 22.If 3 notebooks cost ₹12, how much do 12 notebooks cost? (a) ₹21 (b) ₹144 (c) ₹52 (d) ₹48
  23. 23.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹13 (b) ₹18 (c) ₹60 (d) ₹15
  24. 24.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 11 days (d) 5 days
  25. 25.If 3 notebooks cost ₹66, how much do 2 notebooks cost? (a) ₹65 (b) ₹132 (c) ₹44 (d) ₹66
  26. 26.If 3 pens cost ₹15, how much do 9 pens cost? (a) ₹135 (b) ₹21 (c) ₹50 (d) ₹45
  27. 27.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 1 day (c) 13 days (d) 22 days
  28. 28.If 2 pens cost ₹50, how much do 4 pens cost? (a) ₹100 (b) ₹125 (c) ₹52 (d) ₹200
  29. 29.If 2 kites cost ₹18, how much do 3 kites cost? (a) ₹54 (b) ₹36 (c) ₹27 (d) ₹19
  30. 30.4 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) 2 days (d) 9 days
  31. 31.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹400 (b) ₹275 (c) ₹50 (d) ₹150
  32. 32.₹144 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹72 (b) ₹84 (c) ₹60 (d) ₹12
  33. 33.If 8 notebooks cost ₹200, how much do 10 notebooks cost? (a) ₹2000 (b) ₹250 (c) ₹202 (d) ₹275
  34. 34.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 15 days (c) 16 days (d) 9 days
  35. 35.₹310 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹217 (d) ₹93
  36. 36.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹31 (b) ₹155 (c) ₹279 (d) ₹248
  37. 37.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹56 (b) ₹96 (c) ₹112 (d) ₹16
  38. 38.If 8 mangoes cost ₹192, how much do 6 mangoes cost? (a) ₹168 (b) ₹144 (c) ₹1152 (d) ₹190
  39. 39.3 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
  40. 40.If 9 mangoes cost ₹126, how much do 3 mangoes cost? (a) ₹56 (b) ₹42 (c) ₹120 (d) ₹378

Answer key

  1. 4 days
  2. ₹200
  3. ₹25
  4. ₹70
  5. ₹63
  6. ₹70
  7. ₹12
  8. 18 days
  9. ₹32
  10. 6 days
  11. ₹48
  12. ₹20
  13. ₹234
  14. ₹84
  15. ₹60
  16. ₹36
  17. 4 days
  18. ₹124
  19. ₹230
  20. ₹222
  21. ₹200
  22. ₹48
  23. ₹15
  24. 12 days
  25. ₹44
  26. ₹45
  27. 21 days
  28. ₹100
  29. ₹27
  30. 8 days
  31. ₹400
  32. ₹84
  33. ₹250
  34. 15 days
  35. ₹217
  36. ₹248
  37. ₹96
  38. ₹144
  39. 3 days
  40. ₹42

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