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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 941 · 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.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹72 (b) ₹32 (c) ₹8 (d) ₹52
  2. 2.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 19 days (d) 40 days
  3. 3.If 9 mangoes cost ₹54, how much do 10 mangoes cost? (a) ₹540 (b) ₹66 (c) ₹55 (d) ₹60
  4. 4.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹220 (b) ₹308 (c) ₹44 (d) ₹396
  5. 5.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 1 day (d) 3 days
  6. 6.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹198 (b) ₹288 (c) ₹108 (d) ₹36
  7. 7.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 10 days (d) 12 days
  8. 8.If 6 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹22 (b) ₹96 (c) ₹16 (d) ₹20
  9. 9.If 5 pens cost ₹55, how much do 9 pens cost? (a) ₹110 (b) ₹59 (c) ₹99 (d) ₹495
  10. 10.₹308 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹196 (b) ₹112 (c) ₹28 (d) ₹154
  11. 11.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹91 (d) ₹13
  12. 12.If 2 mangoes cost ₹50, how much do 5 mangoes cost? (a) ₹53 (b) ₹150 (c) ₹125 (d) ₹250
  13. 13.₹370 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹370 (b) ₹37 (c) ₹333 (d) ₹185
  14. 14.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 7 days
  15. 15.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 13 days (d) 7 days
  16. 16.If 2 pens cost ₹34, how much do 3 pens cost? (a) ₹102 (b) ₹68 (c) ₹35 (d) ₹51
  17. 17.If 4 pens cost ₹32, how much do 12 pens cost? (a) ₹40 (b) ₹104 (c) ₹96 (d) ₹384
  18. 18.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹35 (d) ₹5
  19. 19.₹72 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹40 (c) ₹32 (d) ₹8
  20. 20.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 15 days (d) 9 days
  21. 21.If 4 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹46 (b) ₹96 (c) ₹24 (d) ₹36
  22. 22.If 2 kites cost ₹26, how much do 4 kites cost? (a) ₹65 (b) ₹104 (c) ₹52 (d) ₹28
  23. 23.₹240 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹100 (b) ₹20 (c) ₹140 (d) ₹120
  24. 24.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 8 days (d) 10 days
  25. 25.If 4 kites cost ₹72, how much do 9 kites cost? (a) ₹162 (b) ₹77 (c) ₹180 (d) ₹648
  26. 26.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 3 days
  27. 27.If 3 mangoes cost ₹66, how much do 4 mangoes cost? (a) ₹88 (b) ₹67 (c) ₹110 (d) ₹264
  28. 28.If 2 notebooks cost ₹24, how much do 5 notebooks cost? (a) ₹72 (b) ₹27 (c) ₹120 (d) ₹60
  29. 29.If 2 kites cost ₹36, how much do 10 kites cost? (a) ₹198 (b) ₹360 (c) ₹180 (d) ₹44
  30. 30.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 16 days (d) 11 days
  31. 31.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 5 days
  32. 32.If 6 pens cost ₹102, how much do 7 pens cost? (a) ₹103 (b) ₹714 (c) ₹136 (d) ₹119
  33. 33.₹200 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹200 (b) ₹100 (c) ₹160 (d) ₹40
  34. 34.If 9 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹108 (b) ₹30 (c) ₹12 (d) ₹16
  35. 35.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹39 (b) ₹13 (c) ₹52 (d) ₹26
  36. 36.If 7 kites cost ₹28, how much do 5 kites cost? (a) ₹140 (b) ₹20 (c) ₹24 (d) ₹26
  37. 37.If 6 kites cost ₹150, how much do 2 kites cost? (a) ₹300 (b) ₹50 (c) ₹146 (d) ₹75
  38. 38.If 9 pens cost ₹117, how much do 11 pens cost? (a) ₹143 (b) ₹119 (c) ₹156 (d) ₹1287
  39. 39.If 2 pens cost ₹24, how much do 3 pens cost? (a) ₹72 (b) ₹25 (c) ₹36 (d) ₹48
  40. 40.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹39 (c) ₹78 (d) ₹52

Answer key

  1. ₹72
  2. 39 days
  3. ₹60
  4. ₹396
  5. 3 days
  6. ₹288
  7. 10 days
  8. ₹16
  9. ₹99
  10. ₹196
  11. ₹91
  12. ₹125
  13. ₹333
  14. 3 days
  15. 25 days
  16. ₹51
  17. ₹96
  18. ₹35
  19. ₹40
  20. 14 days
  21. ₹24
  22. ₹52
  23. ₹140
  24. 2 days
  25. ₹162
  26. 7 days
  27. ₹88
  28. ₹60
  29. ₹180
  30. 16 days
  31. 6 days
  32. ₹119
  33. ₹160
  34. ₹12
  35. ₹39
  36. ₹20
  37. ₹50
  38. ₹143
  39. ₹36
  40. ₹52

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