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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 627 · 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. 1.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 1 day (c) 16 days (d) 10 days
  2. 2.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹247 (b) ₹190 (c) ₹304 (d) ₹38
  3. 3.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹28 (b) ₹196 (c) ₹140 (d) ₹252
  4. 4.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 3 days (c) 4 days (d) 9 days
  5. 5.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days
  6. 6.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 10 days (d) 8 days
  7. 7.If 7 mangoes cost ₹49, how much do 10 mangoes cost? (a) ₹52 (b) ₹77 (c) ₹70 (d) ₹490
  8. 8.If 3 mangoes cost ₹36, how much do 9 mangoes cost? (a) ₹108 (b) ₹324 (c) ₹42 (d) ₹120
  9. 9.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 7 days (d) 6 days
  10. 10.If 7 pens cost ₹140, how much do 12 pens cost? (a) ₹1680 (b) ₹260 (c) ₹240 (d) ₹145
  11. 11.If 7 notebooks cost ₹91, how much do 10 notebooks cost? (a) ₹143 (b) ₹94 (c) ₹130 (d) ₹910
  12. 12.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹330 (b) ₹66 (c) ₹56 (d) ₹77
  13. 13.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 2 days (d) 19 days
  14. 14.₹196 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹196 (b) ₹49 (c) ₹147 (d) ₹98
  15. 15.₹120 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹90 (b) ₹60 (c) ₹120 (d) ₹30
  16. 16.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 7 days
  17. 17.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 4 days (d) 12 days
  18. 18.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹24 (b) ₹27 (c) ₹22 (d) ₹168
  19. 19.If 4 mangoes cost ₹52, how much do 2 mangoes cost? (a) ₹104 (b) ₹50 (c) ₹26 (d) ₹39
  20. 20.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹55 (b) ₹11 (c) ₹99 (d) ₹77
  21. 21.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 3 days (d) 2 days
  22. 22.If 5 pens cost ₹60, how much do 6 pens cost? (a) ₹72 (b) ₹61 (c) ₹84 (d) ₹360
  23. 23.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹68 (b) ₹34 (c) ₹51 (d) ₹17
  24. 24.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
  25. 25.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 3 days (d) 15 days
  26. 26.If 8 notebooks cost ₹64, how much do 7 notebooks cost? (a) ₹56 (b) ₹63 (c) ₹448 (d) ₹64
  27. 27.If 5 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹58 (b) ₹180 (c) ₹48 (d) ₹36
  28. 28.If 7 pens cost ₹133, how much do 2 pens cost? (a) ₹38 (b) ₹128 (c) ₹266 (d) ₹57
  29. 29.If 2 kites cost ₹26, how much do 4 kites cost? (a) ₹28 (b) ₹104 (c) ₹65 (d) ₹52
  30. 30.If 5 pens cost ₹60, how much do 11 pens cost? (a) ₹144 (b) ₹660 (c) ₹66 (d) ₹132
  31. 31.If 6 mangoes cost ₹108, how much do 7 mangoes cost? (a) ₹756 (b) ₹126 (c) ₹144 (d) ₹109
  32. 32.If 2 pens cost ₹40, how much do 4 pens cost? (a) ₹160 (b) ₹42 (c) ₹80 (d) ₹100
  33. 33.If 9 notebooks cost ₹171, how much do 8 notebooks cost? (a) ₹171 (b) ₹1368 (c) ₹152 (d) ₹170
  34. 34.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹37 (b) ₹370 (c) ₹74 (d) ₹333
  35. 35.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 25 days (b) 9 days (c) 13 days (d) 17 days
  36. 36.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 52 days (b) 7 days (c) 53 days (d) 19 days
  37. 37.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹88 (c) ₹77 (d) ₹11
  38. 38.If 6 pens cost ₹18, how much do 11 pens cost? (a) ₹23 (b) ₹36 (c) ₹33 (d) ₹198
  39. 39.If 5 pens cost ₹100, how much do 6 pens cost? (a) ₹140 (b) ₹101 (c) ₹120 (d) ₹600
  40. 40.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 13 days (d) 18 days

Answer key

  1. 16 days
  2. ₹304
  3. ₹252
  4. 3 days
  5. 5 days
  6. 9 days
  7. ₹70
  8. ₹108
  9. 6 days
  10. ₹240
  11. ₹130
  12. ₹66
  13. 18 days
  14. ₹147
  15. ₹90
  16. 7 days
  17. 24 days
  18. ₹24
  19. ₹26
  20. ₹99
  21. 12 days
  22. ₹72
  23. ₹51
  24. 16 days
  25. 27 days
  26. ₹56
  27. ₹36
  28. ₹38
  29. ₹52
  30. ₹132
  31. ₹126
  32. ₹80
  33. ₹152
  34. ₹333
  35. 25 days
  36. 52 days
  37. ₹77
  38. ₹33
  39. ₹120
  40. 18 days

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