Question

The denominator of a rational number is greater than its numerator by 3. If numerator is increased by 14 and denominator is decreased by 3, the new number becomes11/4 . What is
the original number?​

Answer 1

Answer:

Let the numerator be x and denominator be x+3.

If numerator is increased by 14 and denominator is decreased by 3, then,

= x+14/x+3-3 = 11/4

= x+14/x = 11/4

= 4(x+14) = 11x

= 4x+56 = 11x

= 4x-11x = -56

= -7x = -56

= x= 8

So, original fraction = x/x+3 = 8/8+3 = 8/11.......

Mark it as brainliest.....

Answer 2

AnswEr :

8/11.

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

The denominator of a rational number is greater than it's numerator by 3. if numerator is increased by 14 and denominator is decreased by 3. the new number becomes 11/4.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The original number.

$\bf{\blue{\underline{\underline{\bf{Explanation\::}}}}}$

Let the numerator be R

Let the denominator be R+3

So,

$\bf{The\:rational\:number=\dfrac{R}{R+3} }$

$\bf{\red{\large{\underline{\underline{\tt{A.T.Q.\::}}}}}}$

$\mapsto\tt{\dfrac{R+14}{R+3-3} =\dfrac{11}{4} }\\\\\\\mapsto\tt{\dfrac{R+14}{R} =\dfrac{11}{4} }\\\\\\\mapsto\tt{4(R+14)=11(R)\:\:\:\:\:\: \underbrace{\bf{Cross-Multiplication}}}}}\\\\\\\mapsto\tt{4R+56=11R}\\\\\\\mapsto\tt{4R-11R=-56}\\\\\\\mapsto\tt{-7R=-56}\\\\\\\mapsto\tt{R=\cancel{\dfrac{-56}{-7} }}\\\\\\\mapsto\tt{\red{R=8}}$

Thus,

$\bf{\underbrace{\bf{The\:rational\:number\:is\:\frac{R}{R+3} =\frac{8}{8+3} =\frac{8}{11}. }}}}}$