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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 425 · 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.₹132 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹12 (b) ₹72 (c) ₹60 (d) ₹66
  2. 2.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹135 (d) ₹120
  3. 3.If 6 kites cost ₹96, how much do 3 kites cost? (a) ₹93 (b) ₹48 (c) ₹288 (d) ₹64
  4. 4.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹55 (d) ₹44
  5. 5.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 12 days (c) 11 days (d) 3 days
  6. 6.If 9 pens cost ₹153, how much do 11 pens cost? (a) ₹1683 (b) ₹204 (c) ₹187 (d) ₹155
  7. 7.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹240 (c) ₹40 (d) ₹220
  8. 8.If 8 pens cost ₹192, how much do 10 pens cost? (a) ₹240 (b) ₹1920 (c) ₹194 (d) ₹264
  9. 9.If 7 pens cost ₹175, how much do 2 pens cost? (a) ₹50 (b) ₹170 (c) ₹75 (d) ₹350
  10. 10.If 3 pens cost ₹27, how much do 4 pens cost? (a) ₹36 (b) ₹108 (c) ₹45 (d) ₹28
  11. 11.₹290 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹290 (b) ₹261 (c) ₹29 (d) ₹145
  12. 12.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 5 days (d) 7 days
  13. 13.If 5 mangoes cost ₹125, how much do 12 mangoes cost? (a) ₹325 (b) ₹300 (c) ₹132 (d) ₹1500
  14. 14.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 5 days (d) 13 days
  15. 15.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 14 days (d) 4 days
  16. 16.If 7 pens cost ₹154, how much do 11 pens cost? (a) ₹264 (b) ₹242 (c) ₹158 (d) ₹1694
  17. 17.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 28 days (d) 7 days
  18. 18.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 13 days (d) 21 days
  19. 19.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 41 days (c) 16 days (d) 40 days
  20. 20.If 2 kites cost ₹34, how much do 3 kites cost? (a) ₹35 (b) ₹68 (c) ₹51 (d) ₹102
  21. 21.If 2 mangoes cost ₹50, how much do 7 mangoes cost? (a) ₹175 (b) ₹55 (c) ₹200 (d) ₹350
  22. 22.If 8 kites cost ₹48, how much do 10 kites cost? (a) ₹50 (b) ₹480 (c) ₹66 (d) ₹60
  23. 23.If 7 kites cost ₹112, how much do 5 kites cost? (a) ₹110 (b) ₹560 (c) ₹80 (d) ₹96
  24. 24.If 3 mangoes cost ₹51, how much do 5 mangoes cost? (a) ₹85 (b) ₹53 (c) ₹102 (d) ₹255
  25. 25.If 7 mangoes cost ₹175, how much do 6 mangoes cost? (a) ₹1050 (b) ₹174 (c) ₹175 (d) ₹150
  26. 26.If 6 pens cost ₹72, how much do 4 pens cost? (a) ₹70 (b) ₹60 (c) ₹288 (d) ₹48
  27. 27.If 7 kites cost ₹70, how much do 9 kites cost? (a) ₹100 (b) ₹630 (c) ₹72 (d) ₹90
  28. 28.If 4 pens cost ₹24, how much do 5 pens cost? (a) ₹120 (b) ₹30 (c) ₹25 (d) ₹36
  29. 29.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 18 days (d) 19 days
  30. 30.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹279 (b) ₹155 (c) ₹248 (d) ₹31
  31. 31.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 3 days (d) 29 days
  32. 32.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 6 days
  33. 33.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 7 days (c) 22 days (d) 15 days
  34. 34.If 5 pens cost ₹115, how much do 6 pens cost? (a) ₹690 (b) ₹116 (c) ₹138 (d) ₹161
  35. 35.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 33 days (d) 32 days
  36. 36.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 6 days (d) 8 days
  37. 37.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹36 (c) ₹54 (d) ₹45
  38. 38.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 32 days (c) 2 days (d) 17 days
  39. 39.If 6 mangoes cost ₹132, how much do 4 mangoes cost? (a) ₹110 (b) ₹88 (c) ₹528 (d) ₹130
  40. 40.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 13 days (d) 26 days

Answer key

  1. ₹72
  2. ₹150
  3. ₹48
  4. ₹55
  5. 3 days
  6. ₹187
  7. ₹240
  8. ₹240
  9. ₹50
  10. ₹36
  11. ₹261
  12. 6 days
  13. ₹300
  14. 20 days
  15. 4 days
  16. ₹242
  17. 7 days
  18. 21 days
  19. 40 days
  20. ₹51
  21. ₹175
  22. ₹60
  23. ₹80
  24. ₹85
  25. ₹150
  26. ₹48
  27. ₹90
  28. ₹30
  29. 18 days
  30. ₹248
  31. 28 days
  32. 3 days
  33. 22 days
  34. ₹138
  35. 32 days
  36. 8 days
  37. ₹54
  38. 2 days
  39. ₹88
  40. 27 days

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