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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 311 · 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 9 mangoes cost ₹189, how much do 6 mangoes cost? (a) ₹147 (b) ₹1134 (c) ₹186 (d) ₹126
  2. 2.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 10 days (d) 16 days
  3. 3.If 3 kites cost ₹60, how much do 8 kites cost? (a) ₹160 (b) ₹65 (c) ₹180 (d) ₹480
  4. 4.If 2 notebooks cost ₹46, how much do 11 notebooks cost? (a) ₹253 (b) ₹506 (c) ₹276 (d) ₹55
  5. 5.If 7 kites cost ₹42, how much do 11 kites cost? (a) ₹66 (b) ₹462 (c) ₹72 (d) ₹46
  6. 6.If 9 mangoes cost ₹144, how much do 3 mangoes cost? (a) ₹64 (b) ₹138 (c) ₹48 (d) ₹432
  7. 7.9 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 27 days (b) 17 days (c) 7 days (d) 28 days
  8. 8.₹390 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹390 (b) ₹351 (c) ₹195 (d) ₹39
  9. 9.If 4 notebooks cost ₹40, how much do 2 notebooks cost? (a) ₹38 (b) ₹20 (c) ₹30 (d) ₹80
  10. 10.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 8 days (d) 7 days
  11. 11.If 2 pens cost ₹16, how much do 9 pens cost? (a) ₹144 (b) ₹80 (c) ₹72 (d) ₹23
  12. 12.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 13 days (d) 6 days
  13. 13.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 11 days
  14. 14.₹130 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹52 (b) ₹26 (c) ₹65 (d) ₹78
  15. 15.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹211 (c) ₹210 (d) ₹245
  16. 16.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 19 days (d) 18 days
  17. 17.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 6 days
  18. 18.If 6 pens cost ₹132, how much do 4 pens cost? (a) ₹130 (b) ₹110 (c) ₹88 (d) ₹528
  19. 19.If 8 notebooks cost ₹176, how much do 3 notebooks cost? (a) ₹88 (b) ₹171 (c) ₹528 (d) ₹66
  20. 20.If 4 pens cost ₹72, how much do 11 pens cost? (a) ₹792 (b) ₹216 (c) ₹198 (d) ₹79
  21. 21.If 5 kites cost ₹50, how much do 10 kites cost? (a) ₹500 (b) ₹100 (c) ₹55 (d) ₹110
  22. 22.If 4 pens cost ₹68, how much do 2 pens cost? (a) ₹51 (b) ₹34 (c) ₹66 (d) ₹136
  23. 23.8 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 17 days (d) 16 days
  24. 24.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹272 (b) ₹34 (c) ₹153 (d) ₹306
  25. 25.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹102 (b) ₹17 (c) ₹68 (d) ₹85
  26. 26.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 3 days (d) 7 days
  27. 27.If 6 pens cost ₹30, how much do 8 pens cost? (a) ₹45 (b) ₹32 (c) ₹240 (d) ₹40
  28. 28.If 8 notebooks cost ₹192, how much do 5 notebooks cost? (a) ₹144 (b) ₹960 (c) ₹120 (d) ₹189
  29. 29.7 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 3 days (c) 29 days (d) 28 days
  30. 30.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 10 days (d) 4 days
  31. 31.₹76 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹19 (b) ₹76 (c) ₹57 (d) ₹38
  32. 32.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹87 (c) ₹129 (d) ₹86
  33. 33.If 9 pens cost ₹117, how much do 10 pens cost? (a) ₹143 (b) ₹1170 (c) ₹118 (d) ₹130
  34. 34.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹64 (d) ₹48
  35. 35.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 6 days (d) 18 days
  36. 36.₹270 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹135 (b) ₹240 (c) ₹30 (d) ₹270
  37. 37.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹147 (c) ₹168 (d) ₹21
  38. 38.If 2 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹60 (b) ₹40 (c) ₹30 (d) ₹21
  39. 39.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹392 (b) ₹245 (c) ₹49 (d) ₹441
  40. 40.If 2 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹112 (b) ₹37 (c) ₹128 (d) ₹224

Answer key

  1. ₹126
  2. 10 days
  3. ₹160
  4. ₹253
  5. ₹66
  6. ₹48
  7. 27 days
  8. ₹351
  9. ₹20
  10. 7 days
  11. ₹72
  12. 5 days
  13. 8 days
  14. ₹78
  15. ₹210
  16. 18 days
  17. 5 days
  18. ₹88
  19. ₹66
  20. ₹198
  21. ₹100
  22. ₹34
  23. 16 days
  24. ₹272
  25. ₹85
  26. 7 days
  27. ₹40
  28. ₹120
  29. 28 days
  30. 10 days
  31. ₹57
  32. ₹86
  33. ₹130
  34. ₹48
  35. 4 days
  36. ₹240
  37. ₹147
  38. ₹30
  39. ₹392
  40. ₹112

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