Question

The numerator of a rational number is less than its denominator by 3. If the numerator becomes three times and the denominator is increased by 20. then the fraction 1/8 becomes Find the original number​

Answer 1

$\huge\boxed{\mathtt\red{QUESTION\::-}}$

The numerator of a rational number is less than its denominator by 3. If the numerator becomes three times and the denominator is increased by 20. then the fraction 1/8 becomes Find the original number.

$\huge\boxed{\mathtt\red{TO\:FIND::-}}$

◑ The required fraction

$\huge\boxed{\mathtt\red{ASSUMPTION\::-}}$

◑ Let the numerator of the fraction be n

so, the denominator is (n+3)

then, the fraction will be :-

$\large\boxed{\mathtt\blue{Fraction=\frac{n}{n+3}}}$

$\huge\boxed{\mathtt\red{SOLVING\::-}}$

➟ Fraction = $\large{\mathtt{\frac{n}{n+3}}}$

According to the Question :-

✒ $\large{\mathtt{\frac{3n}{n+3+20}=\frac{1}{8}}}$

✒ $\large{\mathtt{\frac{3n}{n+23}=\frac{1}{8}}}$

✒ $\large{\mathtt{8×3n=n+23}}$

✒$\large{\mathtt{24n-n=23}}$

✒$\large{\mathtt{23n=23}}$

$\large\boxed{\mathtt\blue{∴n=1}}$

$\huge\boxed{\mathtt\red{ANSWER\::-}}$

The required fraction is :-

✒ $\large{\mathtt{Fraction=\frac{n}{n+3}}}$

✒ $\large{\mathtt{Fraction =\frac{1}{4}}}$

$\large\boxed{\mathtt\green{∴The\: original\: fraction\:is\:\frac{1}{4}}}$