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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 146 · 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 5 notebooks cost ₹35, how much do 3 notebooks cost? (a) ₹33 (b) ₹28 (c) ₹21 (d) ₹105
  2. 2.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹55 (d) ₹40
  3. 3.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
  4. 4.If 9 pens cost ₹45, how much do 10 pens cost? (a) ₹55 (b) ₹46 (c) ₹50 (d) ₹450
  5. 5.If 6 kites cost ₹30, how much do 10 kites cost? (a) ₹300 (b) ₹34 (c) ₹50 (d) ₹55
  6. 6.If 6 kites cost ₹54, how much do 10 kites cost? (a) ₹58 (b) ₹90 (c) ₹540 (d) ₹99
  7. 7.If 4 pens cost ₹72, how much do 7 pens cost? (a) ₹75 (b) ₹126 (c) ₹144 (d) ₹504
  8. 8.₹75 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹30 (d) ₹45
  9. 9.₹301 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹259 (b) ₹43 (c) ₹301 (d) ₹258
  10. 10.₹444 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹222 (b) ₹259 (c) ₹37 (d) ₹185
  11. 11.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 1 day (c) 5 days (d) 7 days
  12. 12.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 3 days (d) 2 days
  13. 13.If 6 kites cost ₹54, how much do 4 kites cost? (a) ₹36 (b) ₹216 (c) ₹45 (d) ₹52
  14. 14.₹126 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹9 (b) ₹81 (c) ₹63 (d) ₹45
  15. 15.If 3 pens cost ₹69, how much do 4 pens cost? (a) ₹70 (b) ₹276 (c) ₹92 (d) ₹115
  16. 16.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹145 (b) ₹116 (c) ₹117 (d) ₹29
  17. 17.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹216 (c) ₹192 (d) ₹240
  18. 18.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 12 days (d) 11 days
  19. 19.If 3 kites cost ₹66, how much do 4 kites cost? (a) ₹110 (b) ₹264 (c) ₹88 (d) ₹67
  20. 20.If 3 pens cost ₹18, how much do 6 pens cost? (a) ₹108 (b) ₹21 (c) ₹42 (d) ₹36
  21. 21.If 3 pens cost ₹42, how much do 5 pens cost? (a) ₹84 (b) ₹210 (c) ₹44 (d) ₹70
  22. 22.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹164 (b) ₹41 (c) ₹410 (d) ₹369
  23. 23.₹135 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹135 (b) ₹15 (c) ₹120 (d) ₹121
  24. 24.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 10 days
  25. 25.If 4 notebooks cost ₹72, how much do 2 notebooks cost? (a) ₹144 (b) ₹36 (c) ₹54 (d) ₹70
  26. 26.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
  27. 27.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 9 days (d) 16 days
  28. 28.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹162 (b) ₹18 (c) ₹72 (d) ₹117
  29. 29.₹408 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹238 (d) ₹204
  30. 30.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 30 days (c) 31 days (d) 9 days
  31. 31.If 4 kites cost ₹68, how much do 5 kites cost? (a) ₹85 (b) ₹69 (c) ₹340 (d) ₹102
  32. 32.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 4 days (d) 3 days
  33. 33.6 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 6 days (d) 24 days
  34. 34.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 11 days (d) 10 days
  35. 35.₹130 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹90 (b) ₹40 (c) ₹65 (d) ₹10
  36. 36.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹72 (b) ₹24 (c) ₹96 (d) ₹84
  37. 37.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹220 (c) ₹240 (d) ₹200
  38. 38.If 8 mangoes cost ₹200, how much do 7 mangoes cost? (a) ₹200 (b) ₹1400 (c) ₹175 (d) ₹199
  39. 39.If 4 notebooks cost ₹20, how much do 9 notebooks cost? (a) ₹25 (b) ₹50 (c) ₹180 (d) ₹45
  40. 40.If 7 mangoes cost ₹126, how much do 12 mangoes cost? (a) ₹131 (b) ₹234 (c) ₹216 (d) ₹1512

Answer key

  1. ₹21
  2. ₹70
  3. 25 days
  4. ₹50
  5. ₹50
  6. ₹90
  7. ₹126
  8. ₹45
  9. ₹258
  10. ₹259
  11. 6 days
  12. 3 days
  13. ₹36
  14. ₹81
  15. ₹92
  16. ₹116
  17. ₹240
  18. 12 days
  19. ₹88
  20. ₹36
  21. ₹70
  22. ₹369
  23. ₹120
  24. 4 days
  25. ₹36
  26. 49 days
  27. 15 days
  28. ₹162
  29. ₹238
  30. 30 days
  31. ₹85
  32. 3 days
  33. 24 days
  34. 10 days
  35. ₹90
  36. ₹96
  37. ₹240
  38. ₹175
  39. ₹45
  40. ₹216

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