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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 65 · 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 8 pens cost ₹184, how much do 3 pens cost? (a) ₹69 (b) ₹92 (c) ₹179 (d) ₹552
  2. 2.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹90 (b) ₹40 (c) ₹65 (d) ₹10
  3. 3.If 9 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹594 (b) ₹66 (c) ₹56 (d) ₹72
  4. 4.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹119 (b) ₹102 (c) ₹306 (d) ₹54
  5. 5.If 3 notebooks cost ₹18, how much do 4 notebooks cost? (a) ₹72 (b) ₹19 (c) ₹24 (d) ₹30
  6. 6.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹17 (b) ₹170 (c) ₹34 (d) ₹153
  7. 7.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹280 (b) ₹315 (c) ₹35 (d) ₹175
  8. 8.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 13 days
  9. 9.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 5 days (c) 6 days (d) 20 days
  10. 10.If 7 mangoes cost ₹140, how much do 2 mangoes cost? (a) ₹135 (b) ₹60 (c) ₹40 (d) ₹280
  11. 11.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹71 (b) ₹105 (c) ₹35 (d) ₹70
  12. 12.If 9 pens cost ₹90, how much do 10 pens cost? (a) ₹900 (b) ₹100 (c) ₹110 (d) ₹91
  13. 13.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹91 (b) ₹52 (c) ₹104 (d) ₹13
  14. 14.If 3 notebooks cost ₹9, how much do 4 notebooks cost? (a) ₹36 (b) ₹10 (c) ₹15 (d) ₹12
  15. 15.If 9 mangoes cost ₹162, how much do 10 mangoes cost? (a) ₹198 (b) ₹1620 (c) ₹163 (d) ₹180
  16. 16.₹143 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹130 (b) ₹117 (c) ₹26 (d) ₹13
  17. 17.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
  18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 11 days
  19. 19.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 2 days (c) 32 days (d) 14 days
  20. 20.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 17 days (c) 11 days (d) 36 days
  21. 21.If 8 mangoes cost ₹160, how much do 5 mangoes cost? (a) ₹120 (b) ₹800 (c) ₹157 (d) ₹100
  22. 22.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 9 days (d) 5 days
  23. 23.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 11 days (d) 17 days
  24. 24.If 3 kites cost ₹57, how much do 8 kites cost? (a) ₹171 (b) ₹62 (c) ₹456 (d) ₹152
  25. 25.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹162 (c) ₹18 (d) ₹90
  26. 26.₹60 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹60 (d) ₹30
  27. 27.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹144 (c) ₹336 (d) ₹240
  28. 28.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 6 days (d) 7 days
  29. 29.If 8 notebooks cost ₹200, how much do 3 notebooks cost? (a) ₹75 (b) ₹195 (c) ₹600 (d) ₹100
  30. 30.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹306 (b) ₹34 (c) ₹272 (d) ₹153
  31. 31.If 5 kites cost ₹125, how much do 4 kites cost? (a) ₹500 (b) ₹100 (c) ₹124 (d) ₹125
  32. 32.If 9 kites cost ₹144, how much do 8 kites cost? (a) ₹144 (b) ₹143 (c) ₹1152 (d) ₹128
  33. 33.If 5 notebooks cost ₹85, how much do 7 notebooks cost? (a) ₹87 (b) ₹136 (c) ₹119 (d) ₹595
  34. 34.If 5 notebooks cost ₹100, how much do 4 notebooks cost? (a) ₹99 (b) ₹100 (c) ₹400 (d) ₹80
  35. 35.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 1 day (c) 13 days (d) 28 days
  36. 36.If 3 mangoes cost ₹66, how much do 2 mangoes cost? (a) ₹66 (b) ₹65 (c) ₹44 (d) ₹132
  37. 37.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹26 (b) ₹130 (c) ₹117 (d) ₹104
  38. 38.₹112 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹56 (c) ₹16 (d) ₹96
  39. 39.₹264 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹220 (b) ₹132 (c) ₹264 (d) ₹44
  40. 40.If 8 notebooks cost ₹128, how much do 3 notebooks cost? (a) ₹64 (b) ₹384 (c) ₹48 (d) ₹123

Answer key

  1. ₹69
  2. ₹90
  3. ₹66
  4. ₹102
  5. ₹24
  6. ₹153
  7. ₹280
  8. 7 days
  9. 5 days
  10. ₹40
  11. ₹70
  12. ₹100
  13. ₹91
  14. ₹12
  15. ₹180
  16. ₹117
  17. 25 days
  18. 3 days
  19. 32 days
  20. 35 days
  21. ₹100
  22. 5 days
  23. 28 days
  24. ₹152
  25. ₹162
  26. ₹45
  27. ₹336
  28. 7 days
  29. ₹75
  30. ₹272
  31. ₹100
  32. ₹128
  33. ₹119
  34. ₹80
  35. 28 days
  36. ₹44
  37. ₹130
  38. ₹96
  39. ₹220
  40. ₹48

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