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Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 75 · 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 pens cost ₹180, how much do 7 pens cost? (a) ₹140 (b) ₹160 (c) ₹1260 (d) ₹178
  2. 2.If 8 kites cost ₹160, how much do 6 kites cost? (a) ₹140 (b) ₹120 (c) ₹158 (d) ₹960
  3. 3.₹100 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹20 (d) ₹80
  4. 4.₹70 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹10 (c) ₹70 (d) ₹60
  5. 5.₹40 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹15 (b) ₹20 (c) ₹5 (d) ₹25
  6. 6.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 45 days (c) 5 days (d) 44 days
  7. 7.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 6 days (c) 5 days (d) 7 days
  8. 8.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 6 days (d) 5 days
  9. 9.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹344 (d) ₹86
  10. 10.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 28 days (d) 9 days
  11. 11.If 6 kites cost ₹24, how much do 7 kites cost? (a) ₹168 (b) ₹25 (c) ₹32 (d) ₹28
  12. 12.If 9 pens cost ₹225, how much do 4 pens cost? (a) ₹220 (b) ₹900 (c) ₹100 (d) ₹125
  13. 13.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹45 (b) ₹18 (c) ₹54 (d) ₹36
  14. 14.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 41 days (c) 16 days (d) 40 days
  15. 15.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 7 days (d) 8 days
  16. 16.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 17 days
  17. 17.If 9 pens cost ₹45, how much do 8 pens cost? (a) ₹360 (b) ₹45 (c) ₹40 (d) ₹44
  18. 18.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹76 (b) ₹266 (c) ₹38 (d) ₹171
  19. 19.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
  20. 20.If 2 mangoes cost ₹50, how much do 6 mangoes cost? (a) ₹300 (b) ₹54 (c) ₹175 (d) ₹150
  21. 21.If 6 pens cost ₹48, how much do 7 pens cost? (a) ₹49 (b) ₹336 (c) ₹64 (d) ₹56
  22. 22.If 8 kites cost ₹88, how much do 4 kites cost? (a) ₹55 (b) ₹84 (c) ₹44 (d) ₹352
  23. 23.If 7 pens cost ₹126, how much do 5 pens cost? (a) ₹124 (b) ₹630 (c) ₹108 (d) ₹90
  24. 24.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 33 days (d) 17 days
  25. 25.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 14 days
  26. 26.If 6 notebooks cost ₹150, how much do 12 notebooks cost? (a) ₹300 (b) ₹1800 (c) ₹325 (d) ₹156
  27. 27.If 3 pens cost ₹51, how much do 8 pens cost? (a) ₹408 (b) ₹56 (c) ₹153 (d) ₹136
  28. 28.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 2 days (d) 9 days
  29. 29.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹369 (b) ₹328 (c) ₹205 (d) ₹41
  30. 30.If 3 pens cost ₹39, how much do 9 pens cost? (a) ₹117 (b) ₹351 (c) ₹45 (d) ₹130
  31. 31.₹96 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹36 (b) ₹48 (c) ₹12 (d) ₹60
  32. 32.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹49 (c) ₹7 (d) ₹28
  33. 33.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 32 days (d) 33 days
  34. 34.If 4 kites cost ₹52, how much do 10 kites cost? (a) ₹143 (b) ₹58 (c) ₹520 (d) ₹130
  35. 35.₹72 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹36 (b) ₹42 (c) ₹30 (d) ₹6
  36. 36.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 19 days (d) 49 days
  37. 37.If 8 mangoes cost ₹128, how much do 12 mangoes cost? (a) ₹132 (b) ₹1536 (c) ₹208 (d) ₹192
  38. 38.7 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) 7 days (d) 8 days
  39. 39.If 5 pens cost ₹110, how much do 4 pens cost? (a) ₹109 (b) ₹110 (c) ₹440 (d) ₹88
  40. 40.6 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 19 days (c) 18 days (d) 14 days

Answer key

  1. ₹140
  2. ₹120
  3. ₹80
  4. ₹60
  5. ₹25
  6. 44 days
  7. 6 days
  8. 5 days
  9. ₹301
  10. 7 days
  11. ₹28
  12. ₹100
  13. ₹54
  14. 40 days
  15. 8 days
  16. 3 days
  17. ₹40
  18. ₹266
  19. 25 days
  20. ₹150
  21. ₹56
  22. ₹44
  23. ₹90
  24. 33 days
  25. 15 days
  26. ₹300
  27. ₹136
  28. 4 days
  29. ₹328
  30. ₹117
  31. ₹60
  32. ₹49
  33. 32 days
  34. ₹130
  35. ₹42
  36. 49 days
  37. ₹192
  38. 7 days
  39. ₹88
  40. 18 days

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