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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 595 · 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.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹135 (b) ₹15 (c) ₹120 (d) ₹75
  2. 2.If 3 pens cost ₹27, how much do 10 pens cost? (a) ₹34 (b) ₹270 (c) ₹99 (d) ₹90
  3. 3.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 13 days (d) 9 days
  4. 4.If 4 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹672 (b) ₹182 (c) ₹168 (d) ₹64
  5. 5.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹34 (b) ₹238 (c) ₹136 (d) ₹187
  6. 6.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 18 days (c) 16 days (d) 8 days
  7. 7.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹294 (b) ₹295 (c) ₹49 (d) ₹343
  8. 8.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 3 days (d) 7 days
  9. 9.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 45 days (c) 46 days (d) 3 days
  10. 10.₹210 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹189 (d) ₹210
  11. 11.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 12 days (d) 2 days
  12. 12.If 7 notebooks cost ₹63, how much do 12 notebooks cost? (a) ₹117 (b) ₹108 (c) ₹68 (d) ₹756
  13. 13.₹91 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹7 (b) ₹70 (c) ₹63 (d) ₹28
  14. 14.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 35 days (d) 19 days
  15. 15.4 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
  16. 16.If 7 notebooks cost ₹161, how much do 8 notebooks cost? (a) ₹184 (b) ₹207 (c) ₹162 (d) ₹1288
  17. 17.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹84 (d) ₹98
  18. 18.If 6 kites cost ₹84, how much do 2 kites cost? (a) ₹28 (b) ₹80 (c) ₹42 (d) ₹168
  19. 19.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 3 days (d) 5 days
  20. 20.If 4 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹46 (b) ₹36 (c) ₹24 (d) ₹96
  21. 21.If 8 pens cost ₹136, how much do 5 pens cost? (a) ₹133 (b) ₹680 (c) ₹85 (d) ₹102
  22. 22.If 3 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹20 (b) ₹13 (c) ₹48 (d) ₹16
  23. 23.₹403 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹279 (b) ₹310 (c) ₹124 (d) ₹31
  24. 24.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
  25. 25.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 5 days
  26. 26.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹42 (b) ₹189 (c) ₹210 (d) ₹168
  27. 27.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 63 days (c) 64 days (d) 21 days
  28. 28.If 9 pens cost ₹63, how much do 4 pens cost? (a) ₹252 (b) ₹28 (c) ₹35 (d) ₹58
  29. 29.If 8 kites cost ₹104, how much do 3 kites cost? (a) ₹312 (b) ₹52 (c) ₹99 (d) ₹39
  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) 2 days (d) 19 days
  31. 31.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 20 days (c) 8 days (d) 42 days
  32. 32.9 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 18 days (d) 13 days
  33. 33.If 8 notebooks cost ₹128, how much do 7 notebooks cost? (a) ₹112 (b) ₹128 (c) ₹896 (d) ₹127
  34. 34.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 10 days (d) 12 days
  35. 35.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 3 days (d) 16 days
  36. 36.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 8 days (d) 1 day
  37. 37.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 5 days (d) 45 days
  38. 38.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 21 days (d) 9 days
  39. 39.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹189 (b) ₹168 (c) ₹21 (d) ₹105
  40. 40.3 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 11 days (d) 16 days

Answer key

  1. ₹120
  2. ₹90
  3. 22 days
  4. ₹168
  5. ₹238
  6. 8 days
  7. ₹294
  8. 10 days
  9. 45 days
  10. ₹189
  11. 3 days
  12. ₹108
  13. ₹63
  14. 35 days
  15. 26 days
  16. ₹184
  17. ₹98
  18. ₹28
  19. 6 days
  20. ₹24
  21. ₹85
  22. ₹16
  23. ₹279
  24. 28 days
  25. 4 days
  26. ₹210
  27. 63 days
  28. ₹28
  29. ₹39
  30. 3 days
  31. 42 days
  32. 18 days
  33. ₹112
  34. 12 days
  35. 15 days
  36. 8 days
  37. 45 days
  38. 6 days
  39. ₹168
  40. 9 days

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