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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 852 · 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 4 pens cost ₹40, how much do 10 pens cost? (a) ₹110 (b) ₹46 (c) ₹100 (d) ₹400
  2. 2.If 3 notebooks cost ₹75, how much do 4 notebooks cost? (a) ₹100 (b) ₹125 (c) ₹76 (d) ₹300
  3. 3.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
  4. 4.If 5 kites cost ₹80, how much do 2 kites cost? (a) ₹77 (b) ₹48 (c) ₹160 (d) ₹32
  5. 5.If 2 mangoes cost ₹42, how much do 3 mangoes cost? (a) ₹84 (b) ₹43 (c) ₹63 (d) ₹126
  6. 6.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 3 days (d) 4 days
  7. 7.If 9 pens cost ₹117, how much do 2 pens cost? (a) ₹234 (b) ₹26 (c) ₹39 (d) ₹110
  8. 8.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹176 (d) ₹198
  9. 9.If 7 pens cost ₹105, how much do 9 pens cost? (a) ₹150 (b) ₹107 (c) ₹945 (d) ₹135
  10. 10.If 8 pens cost ₹32, how much do 10 pens cost? (a) ₹40 (b) ₹44 (c) ₹34 (d) ₹320
  11. 11.If 3 notebooks cost ₹15, how much do 12 notebooks cost? (a) ₹180 (b) ₹65 (c) ₹60 (d) ₹24
  12. 12.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 1 day (d) 21 days
  13. 13.If 8 notebooks cost ₹112, how much do 11 notebooks cost? (a) ₹154 (b) ₹115 (c) ₹168 (d) ₹1232
  14. 14.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 18 days (d) 10 days
  15. 15.If 2 kites cost ₹26, how much do 12 kites cost? (a) ₹312 (b) ₹36 (c) ₹169 (d) ₹156
  16. 16.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 19 days (d) 11 days
  17. 17.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 13 days (d) 15 days
  18. 18.If 8 pens cost ₹40, how much do 5 pens cost? (a) ₹30 (b) ₹37 (c) ₹200 (d) ₹25
  19. 19.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹196 (d) ₹168
  20. 20.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹72 (c) ₹42 (d) ₹12
  21. 21.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 4 days (d) 3 days
  22. 22.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹396 (b) ₹308 (c) ₹44 (d) ₹220
  23. 23.If 9 kites cost ₹63, how much do 3 kites cost? (a) ₹21 (b) ₹57 (c) ₹28 (d) ₹189
  24. 24.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 36 days (c) 4 days (d) 5 days
  25. 25.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 36 days (c) 35 days (d) 17 days
  26. 26.If 7 kites cost ₹98, how much do 6 kites cost? (a) ₹588 (b) ₹98 (c) ₹84 (d) ₹97
  27. 27.If 9 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹288 (b) ₹36 (c) ₹35 (d) ₹32
  28. 28.If 7 kites cost ₹63, how much do 12 kites cost? (a) ₹756 (b) ₹117 (c) ₹68 (d) ₹108
  29. 29.If 9 kites cost ₹72, how much do 3 kites cost? (a) ₹32 (b) ₹66 (c) ₹216 (d) ₹24
  30. 30.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 6 days (d) 5 days
  31. 31.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 12 days (c) 24 days (d) 23 days
  32. 32.If 5 kites cost ₹75, how much do 8 kites cost? (a) ₹135 (b) ₹120 (c) ₹78 (d) ₹600
  33. 33.₹112 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹56 (b) ₹64 (c) ₹48 (d) ₹16
  34. 34.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹91 (d) ₹65
  35. 35.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 5 days (d) 6 days
  36. 36.If 5 kites cost ₹55, how much do 12 kites cost? (a) ₹132 (b) ₹62 (c) ₹143 (d) ₹660
  37. 37.If 9 pens cost ₹81, how much do 3 pens cost? (a) ₹27 (b) ₹36 (c) ₹243 (d) ₹75
  38. 38.If 6 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹70 (b) ₹288 (c) ₹60 (d) ₹48
  39. 39.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 28 days (d) 27 days
  40. 40.If 7 notebooks cost ₹168, how much do 4 notebooks cost? (a) ₹165 (b) ₹120 (c) ₹96 (d) ₹672

Answer key

  1. ₹100
  2. ₹100
  3. 3 days
  4. ₹32
  5. ₹63
  6. 3 days
  7. ₹26
  8. ₹176
  9. ₹135
  10. ₹40
  11. ₹60
  12. 21 days
  13. ₹154
  14. 6 days
  15. ₹156
  16. 27 days
  17. 15 days
  18. ₹25
  19. ₹196
  20. ₹72
  21. 3 days
  22. ₹396
  23. ₹21
  24. 4 days
  25. 35 days
  26. ₹84
  27. ₹32
  28. ₹108
  29. ₹24
  30. 5 days
  31. 24 days
  32. ₹120
  33. ₹64
  34. ₹91
  35. 4 days
  36. ₹132
  37. ₹27
  38. ₹48
  39. 27 days
  40. ₹96

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