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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 696 · 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 2 kites cost ₹14, how much do 10 kites cost? (a) ₹140 (b) ₹70 (c) ₹22 (d) ₹77
  2. 2.If 2 kites cost ₹18, how much do 8 kites cost? (a) ₹72 (b) ₹81 (c) ₹144 (d) ₹24
  3. 3.If 4 kites cost ₹44, how much do 5 kites cost? (a) ₹45 (b) ₹66 (c) ₹220 (d) ₹55
  4. 4.If 8 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹60 (b) ₹45 (c) ₹115 (d) ₹360
  5. 5.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 4 days (c) 6 days (d) 5 days
  6. 6.If 3 pens cost ₹72, how much do 11 pens cost? (a) ₹80 (b) ₹792 (c) ₹288 (d) ₹264
  7. 7.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 10 days (d) 14 days
  8. 8.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 3 days (c) 36 days (d) 15 days
  9. 9.₹370 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹185 (b) ₹111 (c) ₹259 (d) ₹37
  10. 10.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹70 (b) ₹91 (c) ₹112 (d) ₹14
  11. 11.If 7 mangoes cost ₹91, how much do 11 mangoes cost? (a) ₹95 (b) ₹1001 (c) ₹143 (d) ₹156
  12. 12.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹243 (b) ₹189 (c) ₹135 (d) ₹27
  13. 13.If 5 mangoes cost ₹105, how much do 9 mangoes cost? (a) ₹210 (b) ₹189 (c) ₹945 (d) ₹109
  14. 14.If 5 mangoes cost ₹95, how much do 6 mangoes cost? (a) ₹114 (b) ₹96 (c) ₹133 (d) ₹570
  15. 15.If 2 pens cost ₹36, how much do 4 pens cost? (a) ₹144 (b) ₹72 (c) ₹38 (d) ₹90
  16. 16.If 6 pens cost ₹66, how much do 12 pens cost? (a) ₹792 (b) ₹143 (c) ₹72 (d) ₹132
  17. 17.₹195 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹75 (b) ₹135 (c) ₹15 (d) ₹120
  18. 18.₹42 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹42 (b) ₹14 (c) ₹21 (d) ₹28
  19. 19.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 8 days (d) 9 days
  20. 20.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 2 days (d) 9 days
  21. 21.If 9 notebooks cost ₹99, how much do 5 notebooks cost? (a) ₹95 (b) ₹495 (c) ₹55 (d) ₹66
  22. 22.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 10 days (c) 2 days (d) 14 days
  23. 23.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
  24. 24.If 8 notebooks cost ₹120, how much do 5 notebooks cost? (a) ₹600 (b) ₹117 (c) ₹90 (d) ₹75
  25. 25.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 20 days (d) 21 days
  26. 26.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 17 days (d) 8 days
  27. 27.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 7 days (c) 19 days (d) 40 days
  28. 28.If 5 pens cost ₹125, how much do 10 pens cost? (a) ₹250 (b) ₹275 (c) ₹1250 (d) ₹130
  29. 29.₹77 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹56 (d) ₹7
  30. 30.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 9 days (d) 21 days
  31. 31.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 14 days (d) 9 days
  32. 32.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 23 days (c) 22 days (d) 14 days
  33. 33.If 3 kites cost ₹66, how much do 9 kites cost? (a) ₹72 (b) ₹594 (c) ₹220 (d) ₹198
  34. 34.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹128 (b) ₹160 (c) ₹32 (d) ₹80
  35. 35.₹165 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹15 (b) ₹75 (c) ₹105 (d) ₹90
  36. 36.If 2 kites cost ₹30, how much do 4 kites cost? (a) ₹60 (b) ₹32 (c) ₹75 (d) ₹120
  37. 37.If 8 kites cost ₹192, how much do 2 kites cost? (a) ₹186 (b) ₹48 (c) ₹72 (d) ₹384
  38. 38.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹168 (b) ₹189 (c) ₹105 (d) ₹21
  39. 39.If 9 pens cost ₹225, how much do 4 pens cost? (a) ₹100 (b) ₹900 (c) ₹125 (d) ₹220
  40. 40.₹185 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹74 (b) ₹37 (c) ₹111 (d) ₹148

Answer key

  1. ₹70
  2. ₹72
  3. ₹55
  4. ₹45
  5. 5 days
  6. ₹264
  7. 14 days
  8. 36 days
  9. ₹259
  10. ₹112
  11. ₹143
  12. ₹243
  13. ₹189
  14. ₹114
  15. ₹72
  16. ₹132
  17. ₹120
  18. ₹28
  19. 8 days
  20. 8 days
  21. ₹55
  22. 14 days
  23. 3 days
  24. ₹75
  25. 20 days
  26. 7 days
  27. 39 days
  28. ₹250
  29. ₹56
  30. 5 days
  31. 16 days
  32. 22 days
  33. ₹198
  34. ₹128
  35. ₹90
  36. ₹60
  37. ₹48
  38. ₹168
  39. ₹100
  40. ₹111

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