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 ,the new rational number becomes 1/8 . find the original rational number.​

Answer 1

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Step-by-step explanation:

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• 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 ,the new rational number becomes 1/8

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• The original Rational number

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• Let the numerator of the rational number be x

• So, denominator will be x + 3

• Given in the question that the numerator becomes three times and the denominator is increased by 20 ,the new rational number becomes 1/8

• So, Eqation :-

• $\bf \frac {3x}{x+3+20} = \frac{1}{8}$

• $\bf \frac{3x}{x+23} = \frac{1}{8}$

• $\sf {Do\:Cross\:Multiplication}$

• $\bf 8(3x) = 1 × (x + 23)$

• $\bf 24x = x + 23$

• $\sf Now\:Bring\:x\:Terms\:To\:Right\:Side$

• $\bf 24x - x = 23$

• $\bf 23x = 23$

• $\bf x = \frac{23}{23}$

• $\bf x = 1$

So, we got x as 1.

First we assumed that the numerator will be x and Denominator will be x + 3

• So, Numerator = x = 1

• Denominator = x + 3 = 1 + 3 = 4

So, Rational number :- $\bf \frac{1}{4}$

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