Question

The sum of the numerator and the denominator of a given fraction is 12. If 3 is added to its denominator,
then the fraction becomes a Find the given fraction.
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Answer 1

Correct Question :-

The sum of numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

SoluTion :-

$\sf {Let\ the\ required\ fraction\ be\ \frac{x}{y}.\ Then,}\\\\\\\sf {x+y=12\ .....(1)}\\\\\\\\\sf {And,\ \frac{x}{y+3} =\frac{1}{2} }\\\\\\\sf {2x-y=3\ .....(2)}\\\\\\\\\sf {Adding\ 1\ and\ 2,\ we\ get,}\\\\\\\sf {x=5}\\\\\\\\\sf {Putting\ x=5\ in\ equation\ 1,\ we\ get,}\\\\\\\sf {y=7}\\\\\\\sf {\mapsto Required\ fraction = \frac{7}{5}}$