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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 557 · 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. 1.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 8 days (d) 9 days
  2. 2.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 17 days (d) 9 days
  3. 3.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 9 days (d) 6 days
  4. 4.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 15 days (d) 16 days
  5. 5.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 14 days (d) 11 days
  6. 6.If 2 kites cost ₹50, how much do 8 kites cost? (a) ₹56 (b) ₹400 (c) ₹200 (d) ₹225
  7. 7.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 6 days (c) 4 days (d) 18 days
  8. 8.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 19 days (c) 2 days (d) 12 days
  9. 9.If 9 kites cost ₹27, how much do 5 kites cost? (a) ₹15 (b) ₹18 (c) ₹135 (d) ₹23
  10. 10.If 2 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹462 (b) ₹51 (c) ₹252 (d) ₹231
  11. 11.6 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 31 days (d) 30 days
  12. 12.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 3 days (d) 6 days
  13. 13.If 2 kites cost ₹40, how much do 3 kites cost? (a) ₹80 (b) ₹60 (c) ₹41 (d) ₹120
  14. 14.If 7 pens cost ₹63, how much do 3 pens cost? (a) ₹189 (b) ₹27 (c) ₹36 (d) ₹59
  15. 15.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
  16. 16.If 4 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹41 (b) ₹90 (c) ₹81 (d) ₹324
  17. 17.If 7 pens cost ₹56, how much do 12 pens cost? (a) ₹96 (b) ₹104 (c) ₹672 (d) ₹61
  18. 18.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹108 (d) ₹54
  19. 19.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 20 days (d) 4 days
  20. 20.If 9 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹28 (b) ₹252 (c) ₹42 (d) ₹119
  21. 21.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹450 (c) ₹50 (d) ₹250
  22. 22.If 3 pens cost ₹27, how much do 10 pens cost? (a) ₹99 (b) ₹34 (c) ₹90 (d) ₹270
  23. 23.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 4 days (c) 3 days (d) 9 days
  24. 24.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 19 days (c) 11 days (d) 35 days
  25. 25.₹66 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹33 (b) ₹66 (c) ₹11 (d) ₹55
  26. 26.If 9 kites cost ₹72, how much do 10 kites cost? (a) ₹720 (b) ₹88 (c) ₹73 (d) ₹80
  27. 27.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹89 (b) ₹88 (c) ₹11 (d) ₹99
  28. 28.₹185 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹149 (b) ₹148 (c) ₹37 (d) ₹185
  29. 29.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹60 (b) ₹70 (c) ₹35 (d) ₹10
  30. 30.If 4 mangoes cost ₹64, how much do 12 mangoes cost? (a) ₹768 (b) ₹192 (c) ₹72 (d) ₹208
  31. 31.7 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 17 days (c) 42 days (d) 7 days
  32. 32.If 9 kites cost ₹63, how much do 10 kites cost? (a) ₹70 (b) ₹64 (c) ₹630 (d) ₹77
  33. 33.If 9 pens cost ₹207, how much do 6 pens cost? (a) ₹161 (b) ₹138 (c) ₹204 (d) ₹1242
  34. 34.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 26 days (d) 15 days
  35. 35.If 2 pens cost ₹30, how much do 12 pens cost? (a) ₹360 (b) ₹195 (c) ₹40 (d) ₹180
  36. 36.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 31 days (c) 17 days (d) 13 days
  37. 37.If 5 pens cost ₹100, how much do 6 pens cost? (a) ₹120 (b) ₹140 (c) ₹101 (d) ₹600
  38. 38.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹37 (d) ₹222
  39. 39.If 2 pens cost ₹28, how much do 11 pens cost? (a) ₹308 (b) ₹37 (c) ₹168 (d) ₹154
  40. 40.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹66 (b) ₹36 (c) ₹96 (d) ₹12

Answer key

  1. 9 days
  2. 25 days
  3. 6 days
  4. 15 days
  5. 14 days
  6. ₹200
  7. 4 days
  8. 18 days
  9. ₹15
  10. ₹231
  11. 30 days
  12. 7 days
  13. ₹60
  14. ₹27
  15. 5 days
  16. ₹81
  17. ₹96
  18. ₹90
  19. 5 days
  20. ₹28
  21. ₹450
  22. ₹90
  23. 3 days
  24. 35 days
  25. ₹55
  26. ₹80
  27. ₹88
  28. ₹148
  29. ₹60
  30. ₹192
  31. 42 days
  32. ₹70
  33. ₹138
  34. 26 days
  35. ₹180
  36. 30 days
  37. ₹120
  38. ₹185
  39. ₹154
  40. ₹96

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