The numerator and denominator of the fraction are in the ratio 15 : 8, if the numerator of the fraction is decreased by 9 and the denominat…

Let the fraction be (x/y). According to the question, x/y = 15/8 ----(I)

Now if x is decreased by 9 and y is increased by 6 then the fraction is (x - 9)/(y + 6) ----(II)

According to the problem (x - 9)/(y + 6) = 1.5 = 3/2 ----(III)

From Equation (I), x = (15/8)y ----(IV)

Putting (IV) in Equation (III) we get

$(\frac{{\left( {\frac{{15}}{8}y} \right)\; - \;9}}{{y\; + \;6}} = \frac{3}{2})$

$(?\frac{{15y\; - \;72}}{{8y\; + \;48}} = \;\frac{3}{2})$

⇒ y = 48

Since y = 48 from Equation (IV) x = (15/8) × 48 = 90

∴ Fraction is 90/48.