Question

The numerator of a rational number is 3 less than its denominator. If the

numerator is multiplied by 3 and denominator is increased by 20, then the new rational number is 1upon8 . Find the original rational number ?

plz ans with method and no foolish answers​

Answer 1

Hope it helps................

Answer 2

★Given★

The numerator of a rational number is 3 less than its denominator. If the numerator is multiplied by 3 and denominator is increased by 20, then the new rational number is $\frac{1}{8}.$

★Solution★

Let, the numerator of the rational number be x.

Then,

the denominator of the rational number = x+3

According to the given condition in the sum,

the new numerator = 3x ,and

the new denominator = (x+3)+ 20= x+23

Given that,

$\frac{3x}{x + 23}$ $=\frac{1}{8}$

By cross multiplying, we get

8(3x) = x+23

⇒24x= x+23

⇒23x = 23

or, x = 1

Therefore, the numerator of the rational number =1 and denominator =1+3=4.

Hence, the original rational number is $\frac{1}{4}.$