Question

The denominator of a fraction in 4 more
than twice the numerator when both the numerator and denominator are decreased by
6, then the denominator becomes 12 times
the numerator
Then the fraction is​

Answer 1

Answer:

Let the numerator and denominator of the fraction be x and y respectively. Then,

Fraction \sf{= x/y}=x/y

It is given that

Denominator =2 (Numerator) +4

$\sf{⇒y=2x+4}⇒y=2x+4</p><p></p><p>\sf{⇒2x−y+4=0}⇒2x−y+4=0</p><p></p><p>According to the given condition, we have</p><p></p><p>\sf{y−6=12(x−6)}y−6=12(x−6)</p><p></p><p>\sf{⇒y−6=12x−72}⇒y−6=12x−72</p><p></p><p>\sf{⇒12x−y−66=0}⇒12x−y−66=0</p><p></p><p>Thus, we have the following system of equations</p><p></p><p>\sf{2x−y+4=0 .(i)}2x−y+4=0 .(i)</p><p></p><p>\sf{⇒12x−y−66=0}⇒12x−y−66=0</p><p></p><p>Subtracting equation (i) from equation (ii), we get</p><p></p><p>\sf{10x−70=0}10x−70=0</p><p></p><p>\sf{⇒x=7}⇒x=7</p><p></p><p>Putting x=7 in equation (i), we get</p><p></p><p>\sf{14 −y+4=0}14−y+4=0</p><p></p><p>\sf{⇒y = 18}⇒y=18</p><p></p><p>Hence, required fraction \sf{=7/18.}=7/18.$