Question

The Numerator of a rational number is less than its denominator by 3 if the number become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number​

Answer 1

Given :-

The Numerator of a rational number is less than its denominator by 3 if the number become three times and the denominator is increased by 20 the new number becomes 1/8

To Find :-

Original number

Solution :-

Let the numeratore be x and denominator will be x + 3

Now

When numerator 3 times and denominator increased by 20

3x/x + 3 + 20 = 1/8

3x/x + 23 = 1/8

8(3x) = 1(x + 23)

24x = x + 23

24x - x = 23

23x = 23

x = 23/23

x = 1

Now, Finding denominator

Denominator = x + 3 = 1 + 3 = 4

Fraction = 1/4

Answer 2

▪ Given :-

• The Numerator of a rational number is less than its denominator by 3.

• If the number become three times and the denominator is increased by 20 the new number becomes 1/8.

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▪ To Find :-

• The Original Number.

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▪ Solution :-

Let, for the original number:

• Numerator be = x

According to the Given Condition:

• Denominator should be = x + 3

So,

Original Fraction in form of x = $\mathtt{\dfrac{x}{x+3}}$

《The number become three times and the denominator is increased by 20》

New Number is of the form $\mathtt{\dfrac{3x}{x+23}}$

According to the Given Condition ;

$\mathtt{\dfrac{3x}{x + 23} = \frac{1}{8} } \\ \\ :\longmapsto \mathtt{24x = x + 23} \\ \\ :\longmapsto \mathtt{24x - x =23 } \\ \\ \mathtt{:\longmapsto 23x = 23} \\ \\ \Large \purple{ :\longmapsto  \underline {\boxed{{\bf x = 1} }}}$

Hence,

Original Number = $\sf\dfrac{1}{1+3}$

$\pink{\sf Original \:\:Number=\dfrac{1}{4}}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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