Q25 of 52 Page 1

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 1/15. Find the fraction.

Let the denominator be q


And the numerator be q - 3


Then the fraction will be;



New denominator = q + 1


As given in the question,





15q2 – 45q = 14q2 – 45q + 14q – 45


15q2 – 14q2 – 14q + 45 = 0


q2 14q + 45 = 0


q2 – 5q – 9q + 45 = 0


q(q – 5) – 9(q – 5) = 0


(q – 5)(q – 9) = 0


q – 5 = 0 or q – 9 = 0


q = 5 or q = 9


When q = 5,


Fraction will be =


When q = 9


Fraction will be =


So,


The fractions are 2/5 or 2/3.


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