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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 625 · 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.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹6 (b) ₹42 (c) ₹30 (d) ₹36
  2. 2.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹44 (d) ₹55
  3. 3.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 9 days (c) 17 days (d) 27 days
  4. 4.If 8 pens cost ₹144, how much do 7 pens cost? (a) ₹1008 (b) ₹144 (c) ₹143 (d) ₹126
  5. 5.If 2 notebooks cost ₹18, how much do 5 notebooks cost? (a) ₹21 (b) ₹90 (c) ₹45 (d) ₹54
  6. 6.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹112 (b) ₹32 (c) ₹192 (d) ₹224
  7. 7.If 3 pens cost ₹51, how much do 9 pens cost? (a) ₹57 (b) ₹459 (c) ₹170 (d) ₹153
  8. 8.If 3 kites cost ₹24, how much do 12 kites cost? (a) ₹104 (b) ₹96 (c) ₹33 (d) ₹288
  9. 9.₹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
  10. 10.If 2 pens cost ₹36, how much do 8 pens cost? (a) ₹42 (b) ₹288 (c) ₹162 (d) ₹144
  11. 11.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 11 days (d) 2 days
  12. 12.If 9 notebooks cost ₹198, how much do 4 notebooks cost? (a) ₹88 (b) ₹110 (c) ₹792 (d) ₹193
  13. 13.If 2 notebooks cost ₹50, how much do 12 notebooks cost? (a) ₹60 (b) ₹300 (c) ₹600 (d) ₹325
  14. 14.₹210 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹126 (b) ₹84 (c) ₹105 (d) ₹42
  15. 15.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 10 days (c) 6 days (d) 14 days
  16. 16.If 7 pens cost ₹147, how much do 4 pens cost? (a) ₹84 (b) ₹144 (c) ₹588 (d) ₹105
  17. 17.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 11 days (d) 15 days
  18. 18.₹96 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹96 (d) ₹72
  19. 19.₹144 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹72 (b) ₹112 (c) ₹16 (d) ₹32
  20. 20.If 4 notebooks cost ₹96, how much do 12 notebooks cost? (a) ₹104 (b) ₹288 (c) ₹312 (d) ₹1152
  21. 21.₹276 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹138 (b) ₹23 (c) ₹115 (d) ₹161
  22. 22.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹66 (b) ₹55 (c) ₹44 (d) ₹11
  23. 23.If 4 mangoes cost ₹32, how much do 10 mangoes cost? (a) ₹38 (b) ₹320 (c) ₹88 (d) ₹80
  24. 24.If 8 pens cost ₹32, how much do 11 pens cost? (a) ₹48 (b) ₹35 (c) ₹352 (d) ₹44
  25. 25.If 8 mangoes cost ₹184, how much do 6 mangoes cost? (a) ₹161 (b) ₹138 (c) ₹1104 (d) ₹182
  26. 26.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹26 (b) ₹169 (c) ₹234 (d) ₹104
  27. 27.If 4 notebooks cost ₹20, how much do 8 notebooks cost? (a) ₹160 (b) ₹45 (c) ₹24 (d) ₹40
  28. 28.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹13 (c) ₹78 (d) ₹79
  29. 29.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹280 (b) ₹40 (c) ₹240 (d) ₹200
  30. 30.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 45 days (c) 21 days (d) 5 days
  31. 31.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 19 days
  32. 32.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹40 (b) ₹260 (c) ₹360 (d) ₹160
  33. 33.If 4 pens cost ₹20, how much do 10 pens cost? (a) ₹50 (b) ₹26 (c) ₹55 (d) ₹200
  34. 34.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 63 days (d) 64 days
  35. 35.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 6 days (d) 15 days
  36. 36.₹108 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹108 (c) ₹54 (d) ₹72
  37. 37.If 6 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹20 (b) ₹22 (c) ₹16 (d) ₹96
  38. 38.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 9 days (d) 7 days
  39. 39.₹136 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹85 (b) ₹51 (c) ₹17 (d) ₹68
  40. 40.₹147 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹105 (b) ₹126 (c) ₹42 (d) ₹21

Answer key

  1. ₹42
  2. ₹66
  3. 26 days
  4. ₹126
  5. ₹45
  6. ₹192
  7. ₹153
  8. ₹96
  9. ₹99
  10. ₹144
  11. 3 days
  12. ₹88
  13. ₹300
  14. ₹126
  15. 24 days
  16. ₹84
  17. 26 days
  18. ₹72
  19. ₹112
  20. ₹288
  21. ₹161
  22. ₹55
  23. ₹80
  24. ₹44
  25. ₹138
  26. ₹234
  27. ₹40
  28. ₹78
  29. ₹280
  30. 45 days
  31. 35 days
  32. ₹360
  33. ₹50
  34. 63 days
  35. 24 days
  36. ₹72
  37. ₹16
  38. 8 days
  39. ₹85
  40. ₹105

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