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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 746 · 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.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹200 (d) ₹275
  2. 2.₹77 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹22 (b) ₹66 (c) ₹55 (d) ₹11
  3. 3.If 5 pens cost ₹100, how much do 2 pens cost? (a) ₹97 (b) ₹60 (c) ₹200 (d) ₹40
  4. 4.If 9 mangoes cost ₹90, how much do 4 mangoes cost? (a) ₹50 (b) ₹360 (c) ₹85 (d) ₹40
  5. 5.If 5 pens cost ₹90, how much do 2 pens cost? (a) ₹54 (b) ₹87 (c) ₹180 (d) ₹36
  6. 6.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 11 days (d) 1 day
  7. 7.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
  8. 8.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 11 days (d) 10 days
  9. 9.If 4 mangoes cost ₹80, how much do 9 mangoes cost? (a) ₹85 (b) ₹200 (c) ₹180 (d) ₹720
  10. 10.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹342 (b) ₹380 (c) ₹38 (d) ₹190
  11. 11.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹33 (b) ₹22 (c) ₹23 (d) ₹11
  12. 12.If 8 kites cost ₹64, how much do 2 kites cost? (a) ₹58 (b) ₹16 (c) ₹24 (d) ₹128
  13. 13.If 8 pens cost ₹56, how much do 10 pens cost? (a) ₹58 (b) ₹560 (c) ₹77 (d) ₹70
  14. 14.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 9 days
  15. 15.If 3 pens cost ₹72, how much do 10 pens cost? (a) ₹240 (b) ₹720 (c) ₹79 (d) ₹264
  16. 16.If 6 pens cost ₹78, how much do 9 pens cost? (a) ₹81 (b) ₹130 (c) ₹117 (d) ₹702
  17. 17.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 12 days (d) 2 days
  18. 18.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 3 days (d) 8 days
  19. 19.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 3 days
  20. 20.If 7 pens cost ₹63, how much do 5 pens cost? (a) ₹61 (b) ₹45 (c) ₹54 (d) ₹315
  21. 21.If 7 mangoes cost ₹56, how much do 8 mangoes cost? (a) ₹448 (b) ₹57 (c) ₹72 (d) ₹64
  22. 22.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 18 days (d) 15 days
  23. 23.If 8 notebooks cost ₹80, how much do 10 notebooks cost? (a) ₹110 (b) ₹82 (c) ₹100 (d) ₹800
  24. 24.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹40 (b) ₹140 (c) ₹120 (d) ₹160
  25. 25.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 8 days (d) 9 days
  26. 26.If 6 kites cost ₹90, how much do 7 kites cost? (a) ₹630 (b) ₹105 (c) ₹91 (d) ₹120
  27. 27.If 8 pens cost ₹48, how much do 9 pens cost? (a) ₹49 (b) ₹54 (c) ₹60 (d) ₹432
  28. 28.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹400 (d) ₹360
  29. 29.₹273 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹210 (b) ₹21 (c) ₹84 (d) ₹189
  30. 30.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹297 (d) ₹264
  31. 31.If 4 notebooks cost ₹40, how much do 8 notebooks cost? (a) ₹320 (b) ₹80 (c) ₹90 (d) ₹44
  32. 32.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 13 days (d) 6 days
  33. 33.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹70 (c) ₹10 (d) ₹60
  34. 34.₹264 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹144 (b) ₹24 (c) ₹132 (d) ₹120
  35. 35.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹48 (b) ₹36 (c) ₹24 (d) ₹72
  36. 36.If 2 kites cost ₹26, how much do 10 kites cost? (a) ₹143 (b) ₹34 (c) ₹260 (d) ₹130
  37. 37.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 4 days (c) 16 days (d) 41 days
  38. 38.If 2 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹216 (b) ₹396 (c) ₹198 (d) ₹45
  39. 39.If 3 kites cost ₹24, how much do 4 kites cost? (a) ₹25 (b) ₹40 (c) ₹96 (d) ₹32
  40. 40.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 14 days (c) 32 days (d) 2 days

Answer key

  1. ₹350
  2. ₹55
  3. ₹40
  4. ₹40
  5. ₹36
  6. 2 days
  7. 5 days
  8. 10 days
  9. ₹180
  10. ₹342
  11. ₹22
  12. ₹16
  13. ₹70
  14. 5 days
  15. ₹240
  16. ₹117
  17. 2 days
  18. 7 days
  19. 5 days
  20. ₹45
  21. ₹64
  22. 18 days
  23. ₹100
  24. ₹160
  25. 9 days
  26. ₹105
  27. ₹54
  28. ₹360
  29. ₹189
  30. ₹264
  31. ₹80
  32. 6 days
  33. ₹70
  34. ₹144
  35. ₹48
  36. ₹130
  37. 40 days
  38. ₹198
  39. ₹32
  40. 32 days

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