Question

1. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased
by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the number.
​

Answer 1

$\bf{\Huge{\boxed{\tt{\red{ANSWER\::}}}}}$

$\bf{\Large{\underline{\sf{Given\::}}}}$

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The number.

$\bf{\Large{\underline{\rm{\green{Explanation\::}}}}}$

Let the numerator of the rational number be R.

Let the denominator be R+8.

$\leadsto\sf{The\:Number\:=\:\frac{R}{R+8} }$

A/q

$\longmapsto\tt{\frac{R+17}{R+8-1} =\frac{3}{2} }$

$\longmapsto\tt{\frac{R+17}{R+7} =\frac{3}{2} }$

Cross Multiplication:

$\longmapsto\tt{2(R+17)=3(R+7)}$

$\longmapsto\tt{2R+34=3R+21}$

$\longmapsto\tt{2R-3R\:=\:21-34}$

$\longmapsto\tt{\cancel{-}R\:=\:\cancel{-}13}$

$\longmapsto\tt{\pink{R\:=\:13}}$

Thus,

$\leadsto\sf{The\:number\:is\:=\:\frac{13}{13+8} }$

$\leadsto\sf{\blue{The\:number\:is\:=\:\frac{13}{21}} }$

Answer 2

Step-by-step explanation:

Let the numerator be 'x'

So, the number will be x /x+8

Given,

The numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.

So, the number would be x+17 / x+8-1 and given in the question that result equals to 3/2

==> x+17 / x+8-1 = 3/2

==> x+17 / x+7 = 3/2

2(x+17) = 3(x+7)

==> 2x + 34 = 3x + 21

==> 2x-3x = 21-34

==> -x = -13

==> x = 13

Hence, the required number is 13.