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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 236 · 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. 1.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 48 days (c) 21 days (d) 3 days
  2. 2.₹140 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹90 (b) ₹50 (c) ₹70 (d) ₹10
  3. 3.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 7 days (d) 10 days
  4. 4.If 7 mangoes cost ₹91, how much do 2 mangoes cost? (a) ₹26 (b) ₹39 (c) ₹182 (d) ₹86
  5. 5.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹68 (c) ₹85 (d) ₹17
  6. 6.If 9 pens cost ₹117, how much do 12 pens cost? (a) ₹120 (b) ₹156 (c) ₹169 (d) ₹1404
  7. 7.If 4 kites cost ₹72, how much do 3 kites cost? (a) ₹216 (b) ₹72 (c) ₹71 (d) ₹54
  8. 8.If 4 notebooks cost ₹16, how much do 5 notebooks cost? (a) ₹17 (b) ₹24 (c) ₹80 (d) ₹20
  9. 9.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 6 days (d) 13 days
  10. 10.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 19 days (d) 4 days
  11. 11.If 2 pens cost ₹42, how much do 8 pens cost? (a) ₹168 (b) ₹48 (c) ₹189 (d) ₹336
  12. 12.If 7 mangoes cost ₹126, how much do 8 mangoes cost? (a) ₹1008 (b) ₹127 (c) ₹144 (d) ₹162
  13. 13.If 2 kites cost ₹42, how much do 12 kites cost? (a) ₹273 (b) ₹252 (c) ₹504 (d) ₹52
  14. 14.6 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 14 days (c) 6 days (d) 30 days
  15. 15.₹279 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹62 (b) ₹31 (c) ₹248 (d) ₹217
  16. 16.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 3 days (d) 8 days
  17. 17.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹261 (b) ₹29 (c) ₹232 (d) ₹145
  18. 18.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 27 days (c) 26 days (d) 17 days
  19. 19.₹231 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹189 (b) ₹21 (c) ₹210 (d) ₹42
  20. 20.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 4 days (d) 11 days
  21. 21.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹176 (b) ₹154 (c) ₹88 (d) ₹22
  22. 22.₹154 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹14 (b) ₹112 (c) ₹77 (d) ₹42
  23. 23.If 2 pens cost ₹44, how much do 6 pens cost? (a) ₹132 (b) ₹154 (c) ₹264 (d) ₹48
  24. 24.If 7 pens cost ₹161, how much do 6 pens cost? (a) ₹161 (b) ₹138 (c) ₹160 (d) ₹966
  25. 25.If 7 notebooks cost ₹63, how much do 6 notebooks cost? (a) ₹378 (b) ₹62 (c) ₹63 (d) ₹54
  26. 26.If 7 kites cost ₹105, how much do 10 kites cost? (a) ₹165 (b) ₹150 (c) ₹1050 (d) ₹108
  27. 27.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 5 days (d) 7 days
  28. 28.If 4 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹63 (b) ₹83 (c) ₹84 (d) ₹252
  29. 29.If 5 notebooks cost ₹60, how much do 10 notebooks cost? (a) ₹132 (b) ₹120 (c) ₹65 (d) ₹600
  30. 30.If 3 pens cost ₹9, how much do 9 pens cost? (a) ₹27 (b) ₹30 (c) ₹81 (d) ₹15
  31. 31.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 12 days
  32. 32.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹132 (b) ₹88 (c) ₹66 (d) ₹44
  33. 33.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹18 (b) ₹162 (c) ₹117 (d) ₹72
  34. 34.If 6 pens cost ₹96, how much do 10 pens cost? (a) ₹100 (b) ₹176 (c) ₹960 (d) ₹160
  35. 35.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹144 (b) ₹96 (c) ₹49 (d) ₹72
  36. 36.If 3 notebooks cost ₹69, how much do 12 notebooks cost? (a) ₹299 (b) ₹276 (c) ₹828 (d) ₹78
  37. 37.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 12 days (d) 13 days
  38. 38.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 10 days (d) 18 days
  39. 39.₹90 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹45 (b) ₹18 (c) ₹72 (d) ₹90
  40. 40.6 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 9 days (d) 13 days

Answer key

  1. 3 days
  2. ₹90
  3. 7 days
  4. ₹26
  5. ₹85
  6. ₹156
  7. ₹54
  8. ₹20
  9. 12 days
  10. 3 days
  11. ₹168
  12. ₹144
  13. ₹252
  14. 30 days
  15. ₹217
  16. 2 days
  17. ₹232
  18. 26 days
  19. ₹189
  20. 10 days
  21. ₹154
  22. ₹112
  23. ₹132
  24. ₹138
  25. ₹54
  26. ₹150
  27. 7 days
  28. ₹63
  29. ₹120
  30. ₹27
  31. 3 days
  32. ₹88
  33. ₹162
  34. ₹160
  35. ₹72
  36. ₹276
  37. 12 days
  38. 28 days
  39. ₹72
  40. 12 days

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