Question

days.
Qu: The numerator of fraction
is 7 less
than the denominator.
If 3 is
added to the numerator
land
a is subtracted
from the
denominator. The
fraction
is
equal
to 3/2 Find
the
fraction?

Answer 1

Let,

"x" represents the numerator

"y" represents the denominator

The numerator of a fraction is 7 less than the denominator

i.e., x = y - 7x=y−7 Equation1

As per the question, we get

$\frac{x \:+ \:3}{y\: -\: 9} = \frac{3}{2}$

$\implies 2(x + 3) = 3(y - 9)$

$\implies 2x + 6 = 3y - 27$

substituting from equation1

$\implies 2(y - 7) + 6 = 3y - 27$

$\implies 2y - 14 + 6 = 3y - 27$

$\implies 2y - 8 = 3y - 27$

$\implies 3y - 2y = 27 - 8$

$\implies \bold{y = 19}$

$∴ \bold{x} = y -7 = 19 - 7 = \bold{12}$

$Thus, \: the \: original \: fraction \: is \\ → \boxed{\bold{\underline{ \frac{12}{19} }}}$

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