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In a Certain Positive Fraction, the Denominator is Greater than the Numerator by 3. If 1 is Subtracted from the Numerator and the Denominator Both, the Fraction Reduces By. Find the Fraction. - ICSE Class 10 - Mathematics

Question

In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by. Find the fraction.

Solution

Let the fraction be x/(x + 3)

When 1 is subtracted from both numerator and denominator, then the fraction be comes (x - 1)/(x + 2)

From the given information we have

x/(x + 3) - 1/14 = (x - 1)/(x + 2)

(14x - x - 3)/(14(x + 3)) = (x - 1)/(x + 2)

(13x +- 3)/(14(x + 3)) = (x - 1)/(x + 2)

(13x - 3)(x + 2) = 14(x^2 + 28x - 42)

x^2 + 5x - 36 = 0

x^2 + 9x - 4x - 36 = 0

x(x + 9)(x - 4) = 0

(x + 9)(x - 4) = 0

x = -9, 4

Since x cannot be negative So x = 4

Hence the fraction is x/(x + 3) = 4/7

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Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 13

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Solution In a Certain Positive Fraction, the Denominator is Greater than the Numerator by 3. If 1 is Subtracted from the Numerator and the Denominator Both, the Fraction Reduces By. Find the Fraction. Concept: Quadratic Equations.
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