Question

The denominator of a fraction is 3 more than the numerator. If 2 is added to the numerator and 5 is added to the denominator, the fraction becomes Find the fraction. 2
But the answer is
$\frac{4}{7}$
​

Answer 1

Answer:

Appropriate Question :-

• The denominator of a fraction is 3 more than the numerator. If 2 is added to the numerator and 5 is added to the denominator, the fraction becomes $\bf \dfrac{1}{2}$. Find the fraction.

[Note : The wrong part in the question is the fraction is ½. ]

Given :-

• The denominator of a fraction is 3 more than the numerator.
• 2 is added to the numerator and 5 is added to the denominator.
• The fraction becomes $\sf \dfrac{1}{2}$.

To Find :-

• What is the fraction.

Solution :-

Let,

$\mapsto \rm{\bold{Numerator =\: x}}$

$\mapsto \rm{\bold{Denominator =\: (x + 3)}}$

Then, the original fraction will be :

$\leadsto \sf \dfrac{Numerator}{Denominator}$

$\leadsto \bf{\dfrac{x}{x + 3}}$

$\pink{\bigstar\: \: \: {\sf\bold{\underline{According\: to\: the\: question\: :-}}}}$

$\implies \sf \dfrac{Numerator + 2}{Denominator + 5} =\: New\: Fraction$

$\implies \sf \dfrac{x + 2}{x + 3 + 5} =\: \dfrac{1}{2}$

$\implies \sf \dfrac{x + 2}{x + 8} =\: \dfrac{1}{2}$

$\pink{\bigstar} \: \: {\bf{By\: doing\: cross\: multiplication\: we\: get\: :-}}$

$\implies \sf 2(x + 2) =\: 1(x + 8)$

$\implies \sf 2x + 4 =\: x + 8$

$\implies \sf 2x - x =\: 8 - 4$

$\implies \sf\bold{\purple{ x =\: 4}}$

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x}{x + 3}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{4}{4 + 3}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{4}{7}}}$

${\small{\bold{\underline{\therefore\: The\: fraction\: is\: \dfrac{4}{7}\: .}}}}$

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VERIFICATION :-

$\leadsto \sf \dfrac{x + 2}{x + 3 + 5} =\: \dfrac{1}{2}$

$\leadsto \sf \dfrac{x + 2}{x + 8} =\: \dfrac{1}{2}$

By putting x = 4 we get,

$\leadsto \sf \dfrac{4 + 2}{4 + 8} =\: \dfrac{1}{2}$

$\leadsto \sf \dfrac{\cancel{6}}{\cancel{12}} =\: \dfrac{1}{2}$

$\leadsto \sf \bold{\green{\dfrac{1}{2} =\: \dfrac{1}{2}}}$

Hence, Verified.

Answer 2

Correct Question :

The denominator of a fraction is 3 more than the numerator.

If 2 is added to the numerator and 5 is added to the denominator, the fraction becomes ½

Find the fraction.

Solution :

• The denominator of a fraction is 3 more than the numerator .

• If 2 is added to the numerator and 5 is added to the denominator, the fraction becomes ½.

Suppose that the numerator of this fraction is f.

Denominator is f + 3 .

The fraction becomes f/f+3.

Now 2 is added to the numerator and 5 is added to the denominator. It now becomes ½.

> ( f + 2)/(f + 8) = ½

> f + 8 = 2f + 4

> f = 4

The fraction becomes 4/(4+3) = 4/7. This is the required answer .

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