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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 813 · 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 6 mangoes cost ₹108, how much do 5 mangoes cost? (a) ₹90 (b) ₹108 (c) ₹107 (d) ₹540
  2. 2.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 19 days (c) 28 days (d) 11 days
  3. 3.If 5 mangoes cost ₹50, how much do 3 mangoes cost? (a) ₹40 (b) ₹48 (c) ₹30 (d) ₹150
  4. 4.If 6 mangoes cost ₹90, how much do 10 mangoes cost? (a) ₹165 (b) ₹150 (c) ₹94 (d) ₹900
  5. 5.If 5 kites cost ₹35, how much do 3 kites cost? (a) ₹33 (b) ₹28 (c) ₹21 (d) ₹105
  6. 6.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 23 days (d) 7 days
  7. 7.₹95 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹19 (b) ₹95 (c) ₹77 (d) ₹76
  8. 8.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 5 days (d) 33 days
  9. 9.If 9 mangoes cost ₹207, how much do 11 mangoes cost? (a) ₹276 (b) ₹209 (c) ₹2277 (d) ₹253
  10. 10.If 7 pens cost ₹42, how much do 11 pens cost? (a) ₹66 (b) ₹46 (c) ₹462 (d) ₹72
  11. 11.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 16 days (d) 17 days
  12. 12.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 9 days (c) 16 days (d) 15 days
  13. 13.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 11 days (d) 7 days
  14. 14.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 17 days (d) 5 days
  15. 15.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹110 (b) ₹88 (c) ₹99 (d) ₹22
  16. 16.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 7 days (d) 8 days
  17. 17.If 3 kites cost ₹24, how much do 10 kites cost? (a) ₹88 (b) ₹31 (c) ₹240 (d) ₹80
  18. 18.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹40 (b) ₹100 (c) ₹20 (d) ₹70
  19. 19.If 2 pens cost ₹26, how much do 7 pens cost? (a) ₹182 (b) ₹31 (c) ₹104 (d) ₹91
  20. 20.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
  21. 21.If 2 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹162 (b) ₹180 (c) ₹324 (d) ₹43
  22. 22.If 9 mangoes cost ₹180, how much do 10 mangoes cost? (a) ₹1800 (b) ₹181 (c) ₹220 (d) ₹200
  23. 23.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 15 days (c) 14 days (d) 9 days
  24. 24.If 5 pens cost ₹60, how much do 8 pens cost? (a) ₹63 (b) ₹96 (c) ₹480 (d) ₹108
  25. 25.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹60 (b) ₹54 (c) ₹432 (d) ₹49
  26. 26.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 22 days (d) 3 days
  27. 27.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 39 days (c) 9 days (d) 40 days
  28. 28.If 8 mangoes cost ₹128, how much do 4 mangoes cost? (a) ₹512 (b) ₹64 (c) ₹80 (d) ₹124
  29. 29.If 4 pens cost ₹36, how much do 6 pens cost? (a) ₹216 (b) ₹38 (c) ₹63 (d) ₹54
  30. 30.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 19 days (d) 2 days
  31. 31.If 9 pens cost ₹207, how much do 4 pens cost? (a) ₹92 (b) ₹828 (c) ₹115 (d) ₹202
  32. 32.If 4 pens cost ₹92, how much do 9 pens cost? (a) ₹97 (b) ₹828 (c) ₹230 (d) ₹207
  33. 33.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 20 days (c) 7 days (d) 5 days
  34. 34.If 3 mangoes cost ₹18, how much do 11 mangoes cost? (a) ₹26 (b) ₹72 (c) ₹66 (d) ₹198
  35. 35.₹324 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹162 (c) ₹180 (d) ₹36
  36. 36.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 17 days
  37. 37.If 9 mangoes cost ₹207, how much do 5 mangoes cost? (a) ₹203 (b) ₹138 (c) ₹1035 (d) ₹115
  38. 38.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹93 (b) ₹23 (c) ₹115 (d) ₹92
  39. 39.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹20 (b) ₹70 (c) ₹80 (d) ₹60
  40. 40.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 36 days (d) 6 days

Answer key

  1. ₹90
  2. 27 days
  3. ₹30
  4. ₹150
  5. ₹21
  6. 5 days
  7. ₹76
  8. 33 days
  9. ₹253
  10. ₹66
  11. 16 days
  12. 15 days
  13. 10 days
  14. 5 days
  15. ₹110
  16. 7 days
  17. ₹80
  18. ₹100
  19. ₹91
  20. 25 days
  21. ₹162
  22. ₹200
  23. 14 days
  24. ₹96
  25. ₹54
  26. 21 days
  27. 39 days
  28. ₹64
  29. ₹54
  30. 3 days
  31. ₹92
  32. ₹207
  33. 20 days
  34. ₹66
  35. ₹180
  36. 12 days
  37. ₹115
  38. ₹92
  39. ₹80
  40. 36 days

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