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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 149 · 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.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹55 (b) ₹27 (c) ₹81 (d) ₹54
  2. 2.If 3 mangoes cost ₹9, how much do 8 mangoes cost? (a) ₹27 (b) ₹72 (c) ₹24 (d) ₹14
  3. 3.If 2 kites cost ₹16, how much do 4 kites cost? (a) ₹64 (b) ₹40 (c) ₹18 (d) ₹32
  4. 4.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 4 days (d) 2 days
  5. 5.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹264 (b) ₹96 (c) ₹432 (d) ₹48
  6. 6.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 6 days
  7. 7.₹200 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹200 (b) ₹25 (c) ₹175 (d) ₹100
  8. 8.If 3 kites cost ₹69, how much do 4 kites cost? (a) ₹115 (b) ₹276 (c) ₹70 (d) ₹92
  9. 9.If 2 notebooks cost ₹36, how much do 3 notebooks cost? (a) ₹37 (b) ₹72 (c) ₹54 (d) ₹108
  10. 10.5 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
  11. 11.If 3 pens cost ₹60, how much do 4 pens cost? (a) ₹240 (b) ₹100 (c) ₹61 (d) ₹80
  12. 12.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹132 (b) ₹144 (c) ₹24 (d) ₹120
  13. 13.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 18 days (d) 10 days
  14. 14.6 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 14 days (b) 4 days (c) 16 days (d) 2 days
  15. 15.₹252 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹126 (b) ₹252 (c) ₹216 (d) ₹36
  16. 16.₹480 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹480 (b) ₹432 (c) ₹240 (d) ₹48
  17. 17.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 8 days (d) 6 days
  18. 18.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 17 days (d) 10 days
  19. 19.9 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
  20. 20.₹490 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹245 (b) ₹147 (c) ₹49 (d) ₹343
  21. 21.If 4 mangoes cost ₹80, how much do 7 mangoes cost? (a) ₹83 (b) ₹160 (c) ₹140 (d) ₹560
  22. 22.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
  23. 23.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹29 (d) ₹145
  24. 24.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 7 days (c) 13 days (d) 4 days
  25. 25.If 2 pens cost ₹48, how much do 9 pens cost? (a) ₹240 (b) ₹55 (c) ₹216 (d) ₹432
  26. 26.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 8 days
  27. 27.If 7 pens cost ₹21, how much do 11 pens cost? (a) ₹231 (b) ₹25 (c) ₹36 (d) ₹33
  28. 28.If 2 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹42 (b) ₹192 (c) ₹384 (d) ₹208
  29. 29.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 1 day (c) 36 days (d) 15 days
  30. 30.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹250 (d) ₹150
  31. 31.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 8 days (d) 11 days
  32. 32.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 21 days (c) 20 days (d) 19 days
  33. 33.If 4 pens cost ₹32, how much do 11 pens cost? (a) ₹39 (b) ₹96 (c) ₹88 (d) ₹352
  34. 34.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 11 days (d) 20 days
  35. 35.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 13 days (d) 9 days
  36. 36.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 12 days (c) 16 days (d) 4 days
  37. 37.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹54 (b) ₹81 (c) ₹27 (d) ₹108
  38. 38.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 15 days (b) 17 days (c) 13 days (d) 16 days
  39. 39.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 16 days
  40. 40.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 45 days (d) 9 days

Answer key

  1. ₹54
  2. ₹24
  3. ₹32
  4. 3 days
  5. ₹432
  6. 4 days
  7. ₹175
  8. ₹92
  9. ₹54
  10. 15 days
  11. ₹80
  12. ₹144
  13. 8 days
  14. 4 days
  15. ₹216
  16. ₹432
  17. 8 days
  18. 16 days
  19. 36 days
  20. ₹343
  21. ₹140
  22. 3 days
  23. ₹232
  24. 25 days
  25. ₹216
  26. 6 days
  27. ₹33
  28. ₹192
  29. 36 days
  30. ₹250
  31. 8 days
  32. 20 days
  33. ₹88
  34. 20 days
  35. 12 days
  36. 16 days
  37. ₹81
  38. 16 days
  39. 18 days
  40. 5 days

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