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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 764 · 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.₹250 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹125 (d) ₹200
  2. 2.If 2 pens cost ₹26, how much do 7 pens cost? (a) ₹31 (b) ₹182 (c) ₹104 (d) ₹91
  3. 3.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹215 (b) ₹172 (c) ₹129 (d) ₹43
  4. 4.If 3 notebooks cost ₹54, how much do 5 notebooks cost? (a) ₹108 (b) ₹90 (c) ₹56 (d) ₹270
  5. 5.If 9 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹216 (b) ₹30 (c) ₹24 (d) ₹49
  6. 6.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹128 (b) ₹32 (c) ₹96 (d) ₹64
  7. 7.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 36 days (c) 5 days (d) 15 days
  8. 8.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 19 days (d) 11 days
  9. 9.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 7 days (d) 8 days
  10. 10.If 5 kites cost ₹15, how much do 11 kites cost? (a) ₹36 (b) ₹33 (c) ₹21 (d) ₹165
  11. 11.₹297 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹231 (b) ₹33 (c) ₹66 (d) ₹264
  12. 12.If 4 mangoes cost ₹44, how much do 5 mangoes cost? (a) ₹45 (b) ₹66 (c) ₹220 (d) ₹55
  13. 13.₹45 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹9 (b) ₹37 (c) ₹45 (d) ₹36
  14. 14.If 6 pens cost ₹72, how much do 8 pens cost? (a) ₹96 (b) ₹74 (c) ₹108 (d) ₹576
  15. 15.If 4 kites cost ₹76, how much do 2 kites cost? (a) ₹74 (b) ₹152 (c) ₹38 (d) ₹57
  16. 16.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 11 days (d) 7 days
  17. 17.If 4 pens cost ₹96, how much do 8 pens cost? (a) ₹192 (b) ₹100 (c) ₹768 (d) ₹216
  18. 18.If 9 mangoes cost ₹207, how much do 6 mangoes cost? (a) ₹1242 (b) ₹161 (c) ₹138 (d) ₹204
  19. 19.If 6 pens cost ₹72, how much do 7 pens cost? (a) ₹96 (b) ₹504 (c) ₹73 (d) ₹84
  20. 20.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 29 days (c) 1 day (d) 28 days
  21. 21.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 34 days (d) 17 days
  22. 22.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 31 days (c) 30 days (d) 16 days
  23. 23.If 8 pens cost ₹104, how much do 3 pens cost? (a) ₹52 (b) ₹99 (c) ₹312 (d) ₹39
  24. 24.If 2 mangoes cost ₹14, how much do 8 mangoes cost? (a) ₹112 (b) ₹20 (c) ₹63 (d) ₹56
  25. 25.₹308 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹140 (b) ₹168 (c) ₹154 (d) ₹28
  26. 26.₹32 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹32 (d) ₹16
  27. 27.If 9 kites cost ₹54, how much do 4 kites cost? (a) ₹49 (b) ₹30 (c) ₹24 (d) ₹216
  28. 28.If 2 pens cost ₹32, how much do 6 pens cost? (a) ₹36 (b) ₹112 (c) ₹96 (d) ₹192
  29. 29.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 25 days (d) 4 days
  30. 30.If 8 notebooks cost ₹80, how much do 3 notebooks cost? (a) ₹240 (b) ₹40 (c) ₹75 (d) ₹30
  31. 31.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹27 (b) ₹72 (c) ₹81 (d) ₹9
  32. 32.If 3 mangoes cost ₹21, how much do 2 mangoes cost? (a) ₹42 (b) ₹20 (c) ₹14 (d) ₹21
  33. 33.If 4 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹63 (b) ₹39 (c) ₹72 (d) ₹252
  34. 34.If 5 mangoes cost ₹120, how much do 8 mangoes cost? (a) ₹123 (b) ₹192 (c) ₹216 (d) ₹960
  35. 35.If 7 notebooks cost ₹35, how much do 9 notebooks cost? (a) ₹37 (b) ₹50 (c) ₹45 (d) ₹315
  36. 36.₹162 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹81 (b) ₹72 (c) ₹18 (d) ₹90
  37. 37.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 4 days (d) 16 days
  38. 38.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 20 days (d) 8 days
  39. 39.If 4 mangoes cost ₹28, how much do 6 mangoes cost? (a) ₹42 (b) ₹168 (c) ₹30 (d) ₹49
  40. 40.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹72 (b) ₹36 (c) ₹8 (d) ₹64

Answer key

  1. ₹200
  2. ₹91
  3. ₹172
  4. ₹90
  5. ₹24
  6. ₹96
  7. 35 days
  8. 45 days
  9. 7 days
  10. ₹33
  11. ₹231
  12. ₹55
  13. ₹36
  14. ₹96
  15. ₹38
  16. 7 days
  17. ₹192
  18. ₹138
  19. ₹84
  20. 28 days
  21. 33 days
  22. 30 days
  23. ₹39
  24. ₹56
  25. ₹168
  26. ₹24
  27. ₹24
  28. ₹96
  29. 25 days
  30. ₹30
  31. ₹72
  32. ₹14
  33. ₹63
  34. ₹192
  35. ₹45
  36. ₹90
  37. 4 days
  38. 20 days
  39. ₹42
  40. ₹64

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