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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 193 · 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 6 kites cost ₹144, how much do 10 kites cost? (a) ₹1440 (b) ₹264 (c) ₹240 (d) ₹148
  2. 2.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹60 (b) ₹108 (c) ₹19 (d) ₹54
  3. 3.9 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
  4. 4.If 6 mangoes cost ₹96, how much do 2 mangoes cost? (a) ₹92 (b) ₹48 (c) ₹32 (d) ₹192
  5. 5.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹15 (b) ₹18 (c) ₹60 (d) ₹13
  6. 6.If 7 kites cost ₹49, how much do 3 kites cost? (a) ₹147 (b) ₹21 (c) ₹45 (d) ₹28
  7. 7.₹378 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹42 (b) ₹294 (c) ₹84 (d) ₹189
  8. 8.₹225 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹25 (b) ₹50 (c) ₹200 (d) ₹175
  9. 9.₹96 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹32 (c) ₹64 (d) ₹96
  10. 10.₹135 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹135 (b) ₹45 (c) ₹90 (d) ₹91
  11. 11.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 10 days (d) 8 days
  12. 12.If 3 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹24 (b) ₹23 (c) ₹48 (d) ₹16
  13. 13.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹65 (b) ₹52 (c) ₹78 (d) ₹13
  14. 14.₹35 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹35 (b) ₹29 (c) ₹28 (d) ₹7
  15. 15.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹35 (d) ₹49
  16. 16.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹242 (b) ₹220 (c) ₹264 (d) ₹44
  17. 17.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 2 days (c) 13 days (d) 1 day
  18. 18.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 2 days (c) 4 days (d) 3 days
  19. 19.If 4 notebooks cost ₹100, how much do 5 notebooks cost? (a) ₹150 (b) ₹101 (c) ₹500 (d) ₹125
  20. 20.If 2 pens cost ₹8, how much do 3 pens cost? (a) ₹9 (b) ₹24 (c) ₹12 (d) ₹16
  21. 21.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
  22. 22.If 9 pens cost ₹117, how much do 5 pens cost? (a) ₹65 (b) ₹585 (c) ₹78 (d) ₹113
  23. 23.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 6 days (d) 7 days
  24. 24.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹26 (d) ₹104
  25. 25.₹121 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹11 (b) ₹66 (c) ₹55 (d) ₹77
  26. 26.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹208 (b) ₹26 (c) ₹104 (d) ₹182
  27. 27.If 2 notebooks cost ₹18, how much do 6 notebooks cost? (a) ₹108 (b) ₹22 (c) ₹54 (d) ₹63
  28. 28.If 4 kites cost ₹88, how much do 2 kites cost? (a) ₹66 (b) ₹86 (c) ₹44 (d) ₹176
  29. 29.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 11 days (d) 14 days
  30. 30.If 8 notebooks cost ₹56, how much do 5 notebooks cost? (a) ₹280 (b) ₹42 (c) ₹35 (d) ₹53
  31. 31.If 9 kites cost ₹180, how much do 5 kites cost? (a) ₹100 (b) ₹900 (c) ₹176 (d) ₹120
  32. 32.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 27 days (c) 26 days (d) 16 days
  33. 33.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 1 day (d) 8 days
  34. 34.If 4 kites cost ₹36, how much do 12 kites cost? (a) ₹44 (b) ₹117 (c) ₹108 (d) ₹432
  35. 35.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹165 (b) ₹198 (c) ₹33 (d) ₹132
  36. 36.If 2 mangoes cost ₹30, how much do 10 mangoes cost? (a) ₹150 (b) ₹165 (c) ₹300 (d) ₹38
  37. 37.If 2 pens cost ₹48, how much do 4 pens cost? (a) ₹50 (b) ₹120 (c) ₹192 (d) ₹96
  38. 38.If 2 mangoes cost ₹20, how much do 7 mangoes cost? (a) ₹80 (b) ₹25 (c) ₹140 (d) ₹70
  39. 39.If 4 mangoes cost ₹56, how much do 10 mangoes cost? (a) ₹62 (b) ₹140 (c) ₹560 (d) ₹154
  40. 40.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 16 days (d) 11 days

Answer key

  1. ₹240
  2. ₹54
  3. 39 days
  4. ₹32
  5. ₹15
  6. ₹21
  7. ₹294
  8. ₹175
  9. ₹64
  10. ₹90
  11. 18 days
  12. ₹16
  13. ₹65
  14. ₹28
  15. ₹49
  16. ₹264
  17. 1 day
  18. 3 days
  19. ₹125
  20. ₹12
  21. 45 days
  22. ₹65
  23. 6 days
  24. ₹91
  25. ₹66
  26. ₹182
  27. ₹54
  28. ₹44
  29. 15 days
  30. ₹35
  31. ₹100
  32. 26 days
  33. 9 days
  34. ₹108
  35. ₹165
  36. ₹150
  37. ₹96
  38. ₹70
  39. ₹140
  40. 15 days

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