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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 718 · 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 4 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹360 (b) ₹108 (c) ₹90 (d) ₹73
  2. 2.If 5 notebooks cost ₹110, how much do 3 notebooks cost? (a) ₹108 (b) ₹66 (c) ₹88 (d) ₹330
  3. 3.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹51 (d) ₹17
  4. 4.If 8 pens cost ₹96, how much do 9 pens cost? (a) ₹97 (b) ₹120 (c) ₹864 (d) ₹108
  5. 5.7 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 29 days (b) 8 days (c) 28 days (d) 16 days
  6. 6.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 2 days (d) 3 days
  7. 7.₹240 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹120 (b) ₹150 (c) ₹90 (d) ₹30
  8. 8.₹430 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹215 (b) ₹43 (c) ₹301 (d) ₹129
  9. 9.If 3 mangoes cost ₹15, how much do 7 mangoes cost? (a) ₹19 (b) ₹35 (c) ₹40 (d) ₹105
  10. 10.₹231 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹99 (b) ₹165 (c) ₹33 (d) ₹132
  11. 11.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 31 days (c) 30 days (d) 17 days
  12. 12.If 3 kites cost ₹54, how much do 4 kites cost? (a) ₹72 (b) ₹55 (c) ₹90 (d) ₹216
  13. 13.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 10 days (d) 3 days
  14. 14.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 3 days (d) 2 days
  15. 15.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹9 (d) ₹27
  16. 16.If 6 pens cost ₹18, how much do 8 pens cost? (a) ₹20 (b) ₹27 (c) ₹24 (d) ₹144
  17. 17.If 5 kites cost ₹30, how much do 4 kites cost? (a) ₹30 (b) ₹29 (c) ₹120 (d) ₹24
  18. 18.If 2 mangoes cost ₹14, how much do 9 mangoes cost? (a) ₹70 (b) ₹63 (c) ₹21 (d) ₹126
  19. 19.If 3 mangoes cost ₹15, how much do 4 mangoes cost? (a) ₹16 (b) ₹25 (c) ₹60 (d) ₹20
  20. 20.If 3 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹252 (b) ₹64 (c) ₹84 (d) ₹105
  21. 21.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 3 days (d) 2 days
  22. 22.₹288 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹120 (b) ₹168 (c) ₹144 (d) ₹24
  23. 23.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 9 days (d) 3 days
  24. 24.If 2 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹60 (b) ₹120 (c) ₹41 (d) ₹80
  25. 25.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹136 (d) ₹119
  26. 26.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 14 days (b) 3 days (c) 4 days (d) 5 days
  27. 27.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 7 days (d) 17 days
  28. 28.If 5 notebooks cost ₹70, how much do 11 notebooks cost? (a) ₹76 (b) ₹168 (c) ₹154 (d) ₹770
  29. 29.If 4 pens cost ₹68, how much do 9 pens cost? (a) ₹73 (b) ₹612 (c) ₹153 (d) ₹170
  30. 30.If 9 pens cost ₹45, how much do 12 pens cost? (a) ₹48 (b) ₹540 (c) ₹65 (d) ₹60
  31. 31.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹45 (d) ₹50
  32. 32.If 4 notebooks cost ₹36, how much do 5 notebooks cost? (a) ₹45 (b) ₹54 (c) ₹37 (d) ₹180
  33. 33.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 10 days (d) 9 days
  34. 34.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
  35. 35.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 8 days
  36. 36.₹231 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹33 (b) ₹66 (c) ₹198 (d) ₹165
  37. 37.If 2 mangoes cost ₹40, how much do 4 mangoes cost? (a) ₹42 (b) ₹80 (c) ₹160 (d) ₹100
  38. 38.If 7 mangoes cost ₹70, how much do 6 mangoes cost? (a) ₹60 (b) ₹70 (c) ₹420 (d) ₹69
  39. 39.If 4 mangoes cost ₹20, how much do 5 mangoes cost? (a) ₹100 (b) ₹25 (c) ₹30 (d) ₹21
  40. 40.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 9 days (d) 4 days

Answer key

  1. ₹90
  2. ₹66
  3. ₹51
  4. ₹108
  5. 28 days
  6. 3 days
  7. ₹150
  8. ₹301
  9. ₹35
  10. ₹132
  11. 30 days
  12. ₹72
  13. 12 days
  14. 3 days
  15. ₹27
  16. ₹24
  17. ₹24
  18. ₹63
  19. ₹20
  20. ₹84
  21. 2 days
  22. ₹168
  23. 9 days
  24. ₹60
  25. ₹119
  26. 4 days
  27. 7 days
  28. ₹154
  29. ₹153
  30. ₹60
  31. ₹45
  32. ₹45
  33. 10 days
  34. 25 days
  35. 12 days
  36. ₹165
  37. ₹80
  38. ₹60
  39. ₹25
  40. 4 days

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