Question

the numerator of a rational number is less than it dominator by 3. if the numerator becomes three and the dominator is increased by 20,the new number becomes 1/8find the number​

Answer 1

Given :

• The numerator of a rational number is less than it denominator by 3

• The numerator increased by three

• The denominator is increased by 20

• The number becomes 1/8

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To find :

• The number =?

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Solution :

Let the numerator of the rational number be x.

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

•According to the given conditions :

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

Given:

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

By cross multiplication we get,

$\implies \sf \: 3x(8) = x + 23 \\ \\ \implies \sf \: 24x = x + 23 \\ \\ \implies \sf \: 24x - x - 23 = 0 \\ \\ \implies \sf \: 23x = 23 \\ \\ \implies \boxed{ \sf{x = 1}}$

• Therefore, numerator of rational number =1

and denominator =1+3=4

$\\ \therefore \rm \: hence \: the \: original \: rational \: number \: \: is \: \frac{1}{4}$