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Problems & Solutions involving Ratio
- 2. PROBLEM1 The sides of a rectangle are in the ratio 4:5. i.By what fraction should the shorter side be increased to make it a square? ii.By what fraction should the longer side be decreased to make it a square?
- 3. SOLUTION πΉππππ ππ πππ ππ = π βΆ π β΄ πΊππππππ πππ π = ππ π³πππππ πππ π = ππ i. π³ππ π ππππ ππ πππ πππππππ πππ π ππ πππππππππ . β΄ π ππππ ππ πππππππ πππ π = π Γ ππ = πππ β΄ π΅ππ πππππππ πππ π = ππ + πππ
- 4. β΄ ππ + πππ βΆ ππ = π βΆ π ππ + πππ ππ = π π ππ + πππ = ππ πππ = ππ β ππ πππ = π π = π ππ β΄ π = π π , πππ ππππππππ ππππππππ.
- 5. ii. πΏππ‘ π ππππ‘ ππ π‘βπ ππππππ π πππ ππ πππππππ ππ. β΄ π ππππ‘ ππ π‘βπ ππππππ π πππ = π Γ 5π₯ = 5ππ₯ β΄ πππ€ ππππππ π πππ = 5π₯ β 5ππ₯ 4π₯ βΆ 5π₯ β 5ππ₯ = 1 βΆ 1
- 6. ππ ππ β πππ = π π β΄ ππ = ππ β πππ πππ = ππ β ππ πππ = π π = π ππ β΄ π = π π , ππ πππ ππππππππ ππππππππ.
- 7. PROBLEM 2 Two quantities are in the ratio 3:5. i. If the smaller alone is made four times the original, what would the ratio be? ii.If the smaller is doubled and the larger is halved, what would the ratio be?
- 8. SOLUTION πΉππππ ππ ππππππππππ = π βΆ π β΄ πΊππππππ ππππππππ = ππ π³πππππ ππππππππ = ππ i. π΅ππ πππππππ ππππππππ = π Γ ππ = πππ π³πππππ ππππππππ = ππ β΄ π΅ππ πππππ = πππ βΆ ππ = ππ βΆ π
- 9. ii. π΅ππ πππππππ ππππππππ = π Γ ππ π΅ππ ππππππ ππππππππ = ππ π π΅ππ πππππ = ππ βΆ ππ π = π βΆ π π = π Γ π βΆ π π Γ π = ππ βΆ π