Question

the denominator of rational number is greater than its numerator by 3 if three subtracted from the numerator and 2 is added to the denominator the new numbers becomes 1/5 find the original number...Answer Fast For 20 Points​

Answer 1

$\large\bf\underline{Given:-}$

• The denominator of rational number is greater than its numerator by 3.
• if three subtracted from the numerator and 2 is added to the denominator the new numbers becomes 1/5

$\large\bf\underline {To \: find:-}$

• Original fraction

$\huge\bf\underline{Solution:-}$

Let the numerator be x

As it is given in the question that the denominator is greater than it's numerator by 3.

so, denominator of fraction is x + 3

According to question :-

if three subtracted from the numerator and 2 is added to the denominator the new numbers becomes 1/5

Numerator becomes = x - 3

Denominator becomes x +3 +2 = x + 5

$: \implies \rm \: \frac{x - 3}{x + 5} = \frac{1}{5} \\ \\ : \implies \rm \:5 (x - 3) = x + 5 \\ \\ : \implies \rm \: 5x - 15 = x + 5 \\ \\ : \implies \rm \: 5x - x = 5 + 15 \\ \\ : \implies \rm \: 4x = 20 \\ \\ : \implies \rm \: x = \cancel\frac{20}{4} \\ \\ : \implies \bf\: x = 5$

So, the numerator of fraction is 5

Denominator = x +3 = 5 +3 = 8

So,

The original fraction is 5/8

Answer 2

✯✯ QUESTION ✯✯

The denominator of rational number is greater than its numerator by 3 if three subtracted from the numerator and 2 is added to the denominator the new numbers becomes 1/5 find the original number...

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Let\:the\:numerator\:be=x}$

➮As Given that the denominator of rational number is greater than its numerator by 2..So ,

$\longmapsto\tt{Denominator\:be=x+3}$

➥A.T.Q : -

If 3 is subracted from numerator and 2 is added to the denominator the new numbers becomes 1/5..

➥So ,

$\longmapsto\tt{Numerator=x-3}$

$\longmapsto\tt{Denominator=x+3+2}$

➥Now ,

$\longmapsto\tt{\dfrac{x-3}{x+3+2}=\dfrac{1}{5}}$

$\longmapsto\tt{5(x-3)=1(x+3+2)}$

$\longmapsto\tt{5x-15=x+3+2}$

$\longmapsto\tt{5x-x=3+2+15}$

$\longmapsto\tt{4x=20}$

$\longmapsto\tt{x=\cancel\dfrac{20}{4}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{5}}}$

_______________________

$\longmapsto\tt{Numerator=x}$

$\longmapsto\tt\bold{5}$

$\longmapsto\tt{Denominator=x+3}$

$\longmapsto\tt{5+3}$

$\longmapsto\tt\bold{8}$

☛So , The numerator is 5 and denominator is 8...

✔The original Fraction is 5/8..