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 number becomes 1/8. Find the original number.
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Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• 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 number becomes 1/8.

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Original number = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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let Numerator be x

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Therefore ; Denominator = x + 3

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Acc. to the given statement :-

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$\sf : \implies\: {\bold{ \dfrac{3x}{x+3+20} = \dfrac{1}{8} }}$

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

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$\sf : \implies\: {\bold{ 8\times 3x = x + 23 }}$

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$\sf : \implies\: {\bold{ 24x = x + 23}}$

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$\sf : \implies\: {\bold{ 24x - x = 23 }}$

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$\sf : \implies\: {\bold{ 23x = 23 }}$

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$\sf : \implies\: {\bold{ x = 1 }}$

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• Putting value of x in the fraction

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Numerator = x = 1

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Denominator = x + 3 = 1 + 3 = 4

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Original fraction = ¼

Answer 2

Hello !

Given :-

• Numerator is 3 less than the denominator
• If the numerator becomes three times and the denominator is increased by 20, the new number becomes 1/8.

To find :-

• The original number.

Solution :-

let the denominator be X.

so, it's numerator becomes x-3.

According to the question:-

$\frac{3(x - 3)}{x + 20} = \frac{1}{8} \\ \frac{3x - 9}{x + 20} = \frac{1}{8} \\ 8(3x - 9) = x + 20 \\ 24x - 72 = x + 20 \\ 23x = 92 \\ x = 4$

Hence, the value of denominator is 4

and numerator is x-3= 4-3 = 1

So the fraction becomes ¼

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Hope it helps ⭐⭐⭐