Question

The numerator of a fraction is 4 les than it's denominator. If the numerator is decreased by 1 the fraction becomes two third. Find the fraction

Answer 1

x-5/x = 2/3 * x-4/x
3x-15=2x -8
x = 7
so fraction is 3/7

Answer 2

Solution..

$let.... \: original \: fraction \: be \: \frac{x}{y} .$

According To the Question ---

▪ The Numerator of a fraction is less than its denominator. So,

x = y - 4.............. Eq. [1.]

And

▪ If the numerator is decreased by 1 then, the fraction becomes two-third. So,

[x - 1 ] / y = 2/3

3x - 3 = 2y........... Eq. [2.]

put value of x in eq.2
we get ,

3 [ y -4 ] - 3 = 2y

3y - 12 - 3 - 2y = 0

______

y = 15.
______

Now put value of y in Eq.[1.]

we get,

x = 15- 4

______

x = 11.
_____

Therefore, Original Fraction is -----

$= \frac{11}{15} \: \: \: ...........is \: the \: required \: answer.$