Question

the numerator of a rational number is less than its denominator by 4.if the numerator is multiplied by 2 and denominator is increased by 4, the number become 14upon 15.find the number​

Answer 1

SOLUTION :

Let the denominator be r

Let the numerator be r - 4

A/q

$\longrightarrow\sf{\dfrac{2(r-4)}{r+4} =\dfrac{14}{15} }\\\\\\\longrightarrow\sf{\dfrac{2r-8}{r+4} =\dfrac{14}{15} }\\\\\\\longrightarrow\sf{15(2r-8)=14(r+4)\:\:\:\underbrace{\sf{Cross-multiplication}}}\\\\\\\longrightarrow\sf{30r-120=14r+56}\\\\\\\longrightarrow\sf{30r-14r=56+120}\\\\\\\longrightarrow\sf{16r=176}\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{176}{16}} }\\\\\\\longrightarrow\bf{r=11}$

Therefore;

$\boxed{\sf{Numerator=r-4=(11-4)=7}}}\\\boxed{\sf{Denominator=r=11}}}$

Thus;

The number will be 7/11 .