Question

deno. of a fraction is 4 more than twice the numerator and denominator decrease by 6 the denominator becomes 12 times the numerator. determine the fraction. ​

Answer 1

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

Fraction =yx

It is given that

Denominator =2 (Numerator) +4

⇒y=2x+4

⇒2x−y+4=0

According to the given condition, we have

y−6=12(x−6)

⇒y−6=12x−72

⇒12x−y−66=0

Thus, we have the following system of equations

2x−y+4=0 .(i)

12x−y−66=0 ..(ii)

Subtracting equation (i) from equation (ii), we get

10x−70=0

⇒x=7

Putting x=7 in equation (i), we get

14−y+4=0

⇒y=18

Hence, required fraction =187.