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If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction?
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If the numerator and denominator of a fraction are both increased by 1...
Solution:
Let the fraction be represented as x/y.
Increasing the numerator and denominator by 1:
(x + 1)/(y + 1) = 3/5
Expanding the equation:
5(x + 1) = 3(y + 1)
5x + 5 = 3y + 3
5x - 3y = -2 ----(i)
Decreasing the numerator and denominator by 1:
(x - 1)/(y - 1) = 5/9
Expanding the equation:
9(x - 1) = 5(y - 1)
9x - 9 = 5y - 5
9x - 5y = 4 ----(ii)
Solving equations (i) and (ii) simultaneously:
5x - 3y = -2 ----(i)
9x - 5y = 4 ----(ii)
Multiplying equation (i) by 3 and equation (ii) by 5:
15x - 9y = -6 ----(iii)
45x - 25y = 20 ----(iv)
Subtracting equation (iii) from equation (iv):
30x - 16y = 26
30(x/y) = 26
x/y = 26/30
x/y = 13/15
Therefore, the fraction is 13/15.
Let the fraction be represented as x/y.
Increasing the numerator and denominator by 1:
(x + 1)/(y + 1) = 3/5
Expanding the equation:
5(x + 1) = 3(y + 1)
5x + 5 = 3y + 3
5x - 3y = -2 ----(i)
Decreasing the numerator and denominator by 1:
(x - 1)/(y - 1) = 5/9
Expanding the equation:
9(x - 1) = 5(y - 1)
9x - 9 = 5y - 5
9x - 5y = 4 ----(ii)
Solving equations (i) and (ii) simultaneously:
5x - 3y = -2 ----(i)
9x - 5y = 4 ----(ii)
Multiplying equation (i) by 3 and equation (ii) by 5:
15x - 9y = -6 ----(iii)
45x - 25y = 20 ----(iv)
Subtracting equation (iii) from equation (iv):
30x - 16y = 26
30(x/y) = 26
x/y = 26/30
x/y = 13/15
Therefore, the fraction is 13/15.
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If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction?
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If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction?.
If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the numerator and denominator of a fraction are both increased by 1, the fraction becomes 3/5. if both are decreased by 1, it becomes 5/9. find the fraction?.
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