Question

The numerator of a rational number is less than its denominator by 3. If the numerator becomes 3 times and denominator is decreased by 20 , the new number is 1/8 . Find the original number.​

Answer 1

Answer:

The original number is $\frac{1}{4}$.

Step-by-step explanation:

Let the numerator of the rational number be x.  

Then, the denominator of the rational number =x+3

According to the given condition,

New numerator =3x and new denominator =(x+3)+20=x+23

Given,  

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

By cross multiplying, we get

8(3x)=x+23

⇒24x=x+23

⇒23x=23 ....[On Transposing]

or x=1

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

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

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