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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 199 · 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 5 mangoes cost ₹75, how much do 3 mangoes cost? (a) ₹225 (b) ₹73 (c) ₹45 (d) ₹60
  2. 2.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹33 (b) ₹77 (c) ₹11 (d) ₹55
  3. 3.₹351 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹270 (d) ₹243
  4. 4.If 7 notebooks cost ₹98, how much do 6 notebooks cost? (a) ₹588 (b) ₹84 (c) ₹98 (d) ₹97
  5. 5.5 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
  6. 6.₹224 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹224 (b) ₹32 (c) ₹112 (d) ₹192
  7. 7.₹261 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹29 (b) ₹174 (c) ₹145 (d) ₹116
  8. 8.If 4 notebooks cost ₹12, how much do 12 notebooks cost? (a) ₹144 (b) ₹39 (c) ₹36 (d) ₹20
  9. 9.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 13 days
  10. 10.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 11 days (d) 2 days
  11. 11.If 4 notebooks cost ₹48, how much do 12 notebooks cost? (a) ₹144 (b) ₹56 (c) ₹576 (d) ₹156
  12. 12.If 7 kites cost ₹28, how much do 8 kites cost? (a) ₹32 (b) ₹36 (c) ₹224 (d) ₹29
  13. 13.If 4 pens cost ₹16, how much do 3 pens cost? (a) ₹48 (b) ₹16 (c) ₹15 (d) ₹12
  14. 14.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹100 (d) ₹60
  15. 15.If 2 mangoes cost ₹44, how much do 9 mangoes cost? (a) ₹220 (b) ₹51 (c) ₹396 (d) ₹198
  16. 16.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 4 days (c) 3 days (d) 15 days
  17. 17.₹360 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹200 (b) ₹180 (c) ₹160 (d) ₹40
  18. 18.₹145 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹117 (b) ₹29 (c) ₹116 (d) ₹145
  19. 19.If 4 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹72 (b) ₹49 (c) ₹240 (d) ₹60
  20. 20.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 14 days (d) 11 days
  21. 21.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 24 days (d) 15 days
  22. 22.If 7 notebooks cost ₹105, how much do 10 notebooks cost? (a) ₹150 (b) ₹165 (c) ₹1050 (d) ₹108
  23. 23.If 3 pens cost ₹12, how much do 4 pens cost? (a) ₹13 (b) ₹20 (c) ₹16 (d) ₹48
  24. 24.If 4 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹60 (b) ₹13 (c) ₹15 (d) ₹18
  25. 25.If 5 notebooks cost ₹115, how much do 10 notebooks cost? (a) ₹230 (b) ₹120 (c) ₹1150 (d) ₹253
  26. 26.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹38 (b) ₹152 (c) ₹133 (d) ₹19
  27. 27.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 2 days (d) 9 days
  28. 28.₹180 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹90 (d) ₹100
  29. 29.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹63 (b) ₹21 (c) ₹126 (d) ₹105
  30. 30.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹344 (b) ₹345 (c) ₹387 (d) ₹43
  31. 31.If 6 mangoes cost ₹60, how much do 5 mangoes cost? (a) ₹50 (b) ₹59 (c) ₹300 (d) ₹60
  32. 32.If 2 notebooks cost ₹34, how much do 3 notebooks cost? (a) ₹68 (b) ₹35 (c) ₹102 (d) ₹51
  33. 33.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 21 days (d) 13 days
  34. 34.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 4 days (d) 9 days
  35. 35.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹205 (b) ₹328 (c) ₹41 (d) ₹369
  36. 36.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹168 (b) ₹42 (c) ₹189 (d) ₹210
  37. 37.If 6 kites cost ₹48, how much do 8 kites cost? (a) ₹50 (b) ₹72 (c) ₹64 (d) ₹384
  38. 38.₹108 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹108 (b) ₹54 (c) ₹90 (d) ₹18
  39. 39.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹16 (b) ₹24 (c) ₹48 (d) ₹32
  40. 40.₹528 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹264 (c) ₹384 (d) ₹144

Answer key

  1. ₹45
  2. ₹77
  3. ₹243
  4. ₹84
  5. 10 days
  6. ₹192
  7. ₹145
  8. ₹36
  9. 7 days
  10. 2 days
  11. ₹144
  12. ₹32
  13. ₹12
  14. ₹100
  15. ₹198
  16. 3 days
  17. ₹200
  18. ₹116
  19. ₹60
  20. 14 days
  21. 6 days
  22. ₹150
  23. ₹16
  24. ₹15
  25. ₹230
  26. ₹133
  27. 8 days
  28. ₹100
  29. ₹105
  30. ₹344
  31. ₹50
  32. ₹51
  33. 21 days
  34. 8 days
  35. ₹328
  36. ₹210
  37. ₹64
  38. ₹90
  39. ₹32
  40. ₹384

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