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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 816 · 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 8 pens cost ₹184, how much do 7 pens cost? (a) ₹161 (b) ₹1288 (c) ₹183 (d) ₹184
  2. 2.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 33 days (c) 15 days (d) 7 days
  3. 3.If 2 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹192 (b) ₹96 (c) ₹108 (d) ₹30
  4. 4.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 52 days (c) 53 days (d) 7 days
  5. 5.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹86 (b) ₹87 (c) ₹43 (d) ₹129
  6. 6.If 5 kites cost ₹25, how much do 4 kites cost? (a) ₹20 (b) ₹25 (c) ₹100 (d) ₹24
  7. 7.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 11 days (d) 7 days
  8. 8.If 7 pens cost ₹112, how much do 8 pens cost? (a) ₹144 (b) ₹113 (c) ₹128 (d) ₹896
  9. 9.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 22 days (c) 21 days (d) 16 days
  10. 10.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
  11. 11.If 7 mangoes cost ₹56, how much do 6 mangoes cost? (a) ₹56 (b) ₹48 (c) ₹336 (d) ₹55
  12. 12.₹35 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹25 (b) ₹15 (c) ₹5 (d) ₹20
  13. 13.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹8 (c) ₹40 (d) ₹48
  14. 14.If 8 kites cost ₹64, how much do 2 kites cost? (a) ₹128 (b) ₹24 (c) ₹58 (d) ₹16
  15. 15.If 2 pens cost ₹12, how much do 5 pens cost? (a) ₹60 (b) ₹30 (c) ₹36 (d) ₹15
  16. 16.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 9 days (d) 10 days
  17. 17.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 20 days (d) 21 days
  18. 18.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 31 days (b) 19 days (c) 30 days (d) 11 days
  19. 19.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 10 days (d) 12 days
  20. 20.If 3 kites cost ₹72, how much do 8 kites cost? (a) ₹192 (b) ₹216 (c) ₹77 (d) ₹576
  21. 21.If 7 kites cost ₹63, how much do 3 kites cost? (a) ₹27 (b) ₹59 (c) ₹189 (d) ₹36
  22. 22.4 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
  23. 23.If 8 kites cost ₹136, how much do 11 kites cost? (a) ₹1496 (b) ₹204 (c) ₹139 (d) ₹187
  24. 24.If 3 mangoes cost ₹51, how much do 6 mangoes cost? (a) ₹119 (b) ₹306 (c) ₹54 (d) ₹102
  25. 25.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 27 days (d) 4 days
  26. 26.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 8 days
  27. 27.₹119 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹17 (b) ₹102 (c) ₹103 (d) ₹119
  28. 28.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 15 days (d) 9 days
  29. 29.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
  30. 30.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 21 days (d) 11 days
  31. 31.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 57 days (c) 8 days (d) 56 days
  32. 32.₹418 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹190 (b) ₹209 (c) ₹228 (d) ₹38
  33. 33.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 11 days (c) 21 days (d) 1 day
  34. 34.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 11 days
  35. 35.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹24 (b) ₹42 (c) ₹6 (d) ₹33
  36. 36.₹315 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹180 (b) ₹135 (c) ₹45 (d) ₹225
  37. 37.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 13 days (c) 1 day (d) 16 days
  38. 38.If 9 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹56 (b) ₹21 (c) ₹14 (d) ₹126
  39. 39.If 5 mangoes cost ₹55, how much do 2 mangoes cost? (a) ₹22 (b) ₹33 (c) ₹110 (d) ₹52
  40. 40.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 11 days (d) 12 days

Answer key

  1. ₹161
  2. 33 days
  3. ₹96
  4. 52 days
  5. ₹86
  6. ₹20
  7. 7 days
  8. ₹128
  9. 21 days
  10. 3 days
  11. ₹48
  12. ₹20
  13. ₹48
  14. ₹16
  15. ₹30
  16. 9 days
  17. 20 days
  18. 30 days
  19. 12 days
  20. ₹192
  21. ₹27
  22. 2 days
  23. ₹187
  24. ₹102
  25. 3 days
  26. 7 days
  27. ₹102
  28. 15 days
  29. 5 days
  30. 21 days
  31. 56 days
  32. ₹228
  33. 21 days
  34. 6 days
  35. ₹42
  36. ₹180
  37. 1 day
  38. ₹14
  39. ₹22
  40. 12 days

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