Question

The denominator of a fraction is 2 more than the numerator.If 1 be added to both the fraction reduces to 4/5.Find the fraction​

Answer 1

Given: The Denominator of a fraction is two more than the Numerator. If 1 is added to Both the Numerator and Denominator then fraction reduces to ⅘.

Need to find: The Original fraction?

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So, Let's Consider that the Numerator of the fraction be x. Then, the Denominator of the fraction be (x + 2) respectively.

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• F r o m⠀G i v e n⠀C o n d i t i o n :

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• Now, we'll add 1 to both the Numerator and Denominator of the fraction, we Get —

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$:\implies\sf \Bigg\{\dfrac{x + 1}{x + 2 + 1}\Bigg\} = \Bigg\{\dfrac{4}{5}\Bigg\} \\\\\\:\implies\sf \Bigg\{\dfrac{x + 1}{x + 3}\Bigg\} = \Bigg\{\dfrac{4}{5}\Bigg\}\\\\\\:\implies\sf 5\Big\{x + 1\Big\} = 4\Big\{x + 3\Big\}\\\\\\:\implies\sf 5x + 5 = 4x + 12\\\\\\:\implies\sf 5x - 4x = 12 - 5\\\\\\:\implies\underline{\boxed{\pmb{\frak{\purple{x = 7}}}}}\;\bigstar$

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Therefore,

• Numerator of fraction, x = 7
• Denominator of fraction, (x + 2) = (7 + 2) = 9

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$\therefore{\underline{\sf{Hence, \: the \: required \: fraction \: is \: {\pmb{\dfrac{7}{9}}.}}}}$

Answer 2

Given :-

The denominator of a fraction is 2 more than the numerator.

If 1 be added to both the fraction reduces to 4/5

To Find :-

Fraction

Solution :-

Let the fraction be a/b

In First condition

b = a + 2(1)

In Second condition

a + 1/b + 1 = 4/5

5(a + 1) = 4(b + 1)

5a + 5 = 4b + 4

5a - 4b = 4 - 5

5a - 4b = -1

Using 1

5a - 4(a + 2) = -1

5a - 4a - 8 = -1

a = 8 - 1

a = 7

Now,

Using 1

b = a + 2

b = 7 + 2

b = 9

Fraction = a/b = 7/9