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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 926 · 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.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹270 (d) ₹243
  2. 2.₹460 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹414 (b) ₹230 (c) ₹46 (d) ₹460
  3. 3.If 8 mangoes cost ₹120, how much do 4 mangoes cost? (a) ₹480 (b) ₹116 (c) ₹60 (d) ₹75
  4. 4.If 8 notebooks cost ₹120, how much do 11 notebooks cost? (a) ₹165 (b) ₹1320 (c) ₹123 (d) ₹180
  5. 5.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 4 days (d) 5 days
  6. 6.₹341 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹124 (b) ₹248 (c) ₹31 (d) ₹217
  7. 7.If 3 notebooks cost ₹60, how much do 6 notebooks cost? (a) ₹140 (b) ₹360 (c) ₹63 (d) ₹120
  8. 8.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 6 days
  9. 9.₹261 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹232 (b) ₹203 (c) ₹58 (d) ₹29
  10. 10.If 9 mangoes cost ₹180, how much do 12 mangoes cost? (a) ₹240 (b) ₹2160 (c) ₹260 (d) ₹183
  11. 11.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹72 (b) ₹18 (c) ₹117 (d) ₹162
  12. 12.If 4 notebooks cost ₹40, how much do 7 notebooks cost? (a) ₹43 (b) ₹280 (c) ₹70 (d) ₹80
  13. 13.₹259 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹222 (b) ₹259 (c) ₹37 (d) ₹223
  14. 14.If 6 notebooks cost ₹108, how much do 5 notebooks cost? (a) ₹540 (b) ₹90 (c) ₹107 (d) ₹108
  15. 15.If 9 pens cost ₹126, how much do 11 pens cost? (a) ₹1386 (b) ₹168 (c) ₹128 (d) ₹154
  16. 16.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 13 days (d) 22 days
  17. 17.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 15 days (b) 7 days (c) 8 days (d) 6 days
  18. 18.If 4 kites cost ₹56, how much do 3 kites cost? (a) ₹42 (b) ₹168 (c) ₹56 (d) ₹55
  19. 19.₹35 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹30 (b) ₹5 (c) ₹31 (d) ₹35
  20. 20.If 5 pens cost ₹60, how much do 3 pens cost? (a) ₹180 (b) ₹48 (c) ₹36 (d) ₹58
  21. 21.₹328 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹41 (b) ₹123 (c) ₹205 (d) ₹164
  22. 22.If 5 notebooks cost ₹75, how much do 7 notebooks cost? (a) ₹77 (b) ₹525 (c) ₹105 (d) ₹120
  23. 23.If 2 kites cost ₹34, how much do 10 kites cost? (a) ₹42 (b) ₹170 (c) ₹187 (d) ₹340
  24. 24.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 10 days (c) 42 days (d) 18 days
  25. 25.₹170 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹85 (b) ₹34 (c) ₹136 (d) ₹170
  26. 26.If 8 pens cost ₹32, how much do 9 pens cost? (a) ₹33 (b) ₹288 (c) ₹36 (d) ₹40
  27. 27.If 8 kites cost ₹120, how much do 4 kites cost? (a) ₹75 (b) ₹480 (c) ₹116 (d) ₹60
  28. 28.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 10 days (d) 5 days
  29. 29.₹63 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹54 (b) ₹9 (c) ₹45 (d) ₹18
  30. 30.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹190 (b) ₹342 (c) ₹380 (d) ₹38
  31. 31.If 8 pens cost ₹120, how much do 10 pens cost? (a) ₹165 (b) ₹122 (c) ₹150 (d) ₹1200
  32. 32.If 5 mangoes cost ₹110, how much do 4 mangoes cost? (a) ₹109 (b) ₹88 (c) ₹440 (d) ₹110
  33. 33.₹245 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹245 (d) ₹197
  34. 34.If 4 mangoes cost ₹20, how much do 5 mangoes cost? (a) ₹25 (b) ₹30 (c) ₹21 (d) ₹100
  35. 35.If 3 pens cost ₹75, how much do 12 pens cost? (a) ₹900 (b) ₹300 (c) ₹325 (d) ₹84
  36. 36.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 14 days
  37. 37.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹60 (b) ₹108 (c) ₹84 (d) ₹12
  38. 38.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 13 days (d) 17 days
  39. 39.If 3 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹48 (b) ₹23 (c) ₹16 (d) ₹24
  40. 40.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹32 (c) ₹24 (d) ₹48

Answer key

  1. ₹243
  2. ₹414
  3. ₹60
  4. ₹165
  5. 6 days
  6. ₹217
  7. ₹120
  8. 7 days
  9. ₹203
  10. ₹240
  11. ₹162
  12. ₹70
  13. ₹222
  14. ₹90
  15. ₹154
  16. 21 days
  17. 7 days
  18. ₹42
  19. ₹30
  20. ₹36
  21. ₹205
  22. ₹105
  23. ₹170
  24. 42 days
  25. ₹136
  26. ₹36
  27. ₹60
  28. 6 days
  29. ₹45
  30. ₹342
  31. ₹150
  32. ₹88
  33. ₹196
  34. ₹25
  35. ₹300
  36. 5 days
  37. ₹108
  38. 16 days
  39. ₹16
  40. ₹32

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