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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 457 · 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.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹124 (b) ₹155 (c) ₹31 (d) ₹186
  2. 2.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹88 (b) ₹110 (c) ₹99 (d) ₹22
  3. 3.If 2 mangoes cost ₹46, how much do 8 mangoes cost? (a) ₹52 (b) ₹368 (c) ₹184 (d) ₹207
  4. 4.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 9 days (d) 11 days
  5. 5.If 3 pens cost ₹48, how much do 4 pens cost? (a) ₹192 (b) ₹49 (c) ₹80 (d) ₹64
  6. 6.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 11 days (d) 9 days
  7. 7.If 6 pens cost ₹36, how much do 10 pens cost? (a) ₹360 (b) ₹40 (c) ₹60 (d) ₹66
  8. 8.If 6 notebooks cost ₹42, how much do 5 notebooks cost? (a) ₹42 (b) ₹210 (c) ₹35 (d) ₹41
  9. 9.If 5 mangoes cost ₹25, how much do 7 mangoes cost? (a) ₹27 (b) ₹175 (c) ₹40 (d) ₹35
  10. 10.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹150 (b) ₹50 (c) ₹200 (d) ₹175
  11. 11.If 2 notebooks cost ₹6, how much do 5 notebooks cost? (a) ₹15 (b) ₹18 (c) ₹30 (d) ₹9
  12. 12.₹245 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹105 (b) ₹35 (c) ₹140 (d) ₹175
  13. 13.If 4 pens cost ₹36, how much do 12 pens cost? (a) ₹44 (b) ₹108 (c) ₹117 (d) ₹432
  14. 14.₹273 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹235 (b) ₹39 (c) ₹273 (d) ₹234
  15. 15.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 17 days (c) 9 days (d) 13 days
  16. 16.If 3 kites cost ₹48, how much do 7 kites cost? (a) ₹128 (b) ₹336 (c) ₹52 (d) ₹112
  17. 17.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹104 (d) ₹128
  18. 18.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
  19. 19.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 13 days (d) 21 days
  20. 20.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹172 (b) ₹215 (c) ₹129 (d) ₹43
  21. 21.₹330 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹240 (d) ₹165
  22. 22.If 2 kites cost ₹46, how much do 4 kites cost? (a) ₹48 (b) ₹92 (c) ₹184 (d) ₹115
  23. 23.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 27 days (c) 28 days (d) 7 days
  24. 24.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 13 days (d) 17 days
  25. 25.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹29 (b) ₹145 (c) ₹261 (d) ₹232
  26. 26.If 7 kites cost ₹56, how much do 10 kites cost? (a) ₹560 (b) ₹88 (c) ₹59 (d) ₹80
  27. 27.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 17 days (d) 16 days
  28. 28.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 13 days
  29. 29.If 9 notebooks cost ₹36, how much do 5 notebooks cost? (a) ₹24 (b) ₹32 (c) ₹180 (d) ₹20
  30. 30.If 5 mangoes cost ₹35, how much do 3 mangoes cost? (a) ₹28 (b) ₹21 (c) ₹105 (d) ₹33
  31. 31.₹105 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹63 (b) ₹42 (c) ₹84 (d) ₹21
  32. 32.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 10 days (d) 9 days
  33. 33.₹287 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹41 (b) ₹123 (c) ₹164 (d) ₹205
  34. 34.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 3 days (c) 4 days (d) 2 days
  35. 35.₹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
  36. 36.If 2 pens cost ₹6, how much do 12 pens cost? (a) ₹72 (b) ₹36 (c) ₹39 (d) ₹16
  37. 37.If 3 pens cost ₹42, how much do 5 pens cost? (a) ₹84 (b) ₹210 (c) ₹44 (d) ₹70
  38. 38.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
  39. 39.If 6 kites cost ₹30, how much do 4 kites cost? (a) ₹20 (b) ₹28 (c) ₹120 (d) ₹25
  40. 40.₹352 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹308 (b) ₹352 (c) ₹176 (d) ₹44

Answer key

  1. ₹155
  2. ₹110
  3. ₹184
  4. 9 days
  5. ₹64
  6. 10 days
  7. ₹60
  8. ₹35
  9. ₹35
  10. ₹200
  11. ₹15
  12. ₹140
  13. ₹108
  14. ₹234
  15. 25 days
  16. ₹112
  17. ₹128
  18. 16 days
  19. 21 days
  20. ₹215
  21. ₹240
  22. ₹92
  23. 27 days
  24. 9 days
  25. ₹232
  26. ₹80
  27. 16 days
  28. 21 days
  29. ₹20
  30. ₹21
  31. ₹63
  32. 9 days
  33. ₹164
  34. 3 days
  35. ₹396
  36. ₹36
  37. ₹70
  38. 39 days
  39. ₹20
  40. ₹308

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