MathematicsThe numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 115. The fraction is ____

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 115. The fraction is ____


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    Solution:

    The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 115. The fraction is 25.
    Given that the numerator of a fraction is 3 less than its denominator.
    Let’s assume that the numerator and denominator are n and d respectively.
    n=d-3            Then,
    nd=d-3d                       … (1)
    After adding 1 to the denominator the fraction decreased by 115
    d-3d+1=115                    … (2)
    To find the fraction we will equate equation (1) and equation (2),
    d-3d-d-3d+1=115 
    d-3d+1-dd-3dd+1=115
    dd+1-3d+1-d2+3dd2+d=115
    d2+d-3d-3-d2+3dd2+d=115
    d-3d2+d=115
    15d-3=d2+d
    15d-45=d2+d
    d2-15d+45=0
    d2-9d-5d+45=0
    dd-9-5d-9=0
    d-5d-9=0
    d-5=0 or d-9=0
     d=5 or d=9 
    If d=5 then,
    n=d-3=5-3=2 Then the fraction is 25.
    If d=9 then,
    n=d-3=9-3=6 Then the fraction is 69=23
    ∴ We will neglect this fraction because it is not satisfying the given condition.
    Hence, the original fraction is 25.                                
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