Question

The denominator of a fraction is 3 more than numerator. If 2 is added to the numerator and 5 is added to the denominator then the fraction becomes 1/2. Finf the fraction ​

Answer 1

Given:

• The denominator of a fraction is 3 more than numerator.
• If 2 is added to the numerator and 5 is added to the denominator then the fraction becomes 1/2.

To find:

• Original Fraction?

Solution:

☯ Let the numerator of a fraction be x.

Then, The denominator of fraction will be (x + 3).

Now,

★ According to the Question:

• 2 is added to numerator = (x + 2)
• 5 is added to denominator = [(x + 3) + 5]

➯ (x + 2)/(x + 3 + 5) = 1/2

➯ (x + 2)/(x + 8) = 1/2

➯ 2(x + 2) = x + 8

➯ 2x + 4 = x + 8

➯ 2x - x = 8 - 4

➯ x = 4

Hence,

• Numerator of the fraction, x = 4
• Denominator of the fraction, (x + 3) = 4 + 3 = 7

∴ Required fraction is 4/7.

Answer 2

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Let the numerator be x and the denominator be ( x + 3 )

Given that :-

If 2 is added to the numerator = ( x + 2 )

and 5 is added to the denominator = ( x + 3 ) + 5

So , the required equation is :-

( x + 2 )( x + 3) + 5 = 1 / 2

( x + 2 ) ( x + 8 ) = 1/2

2 ( x + 2 ) = ( x + 8 )

2x + 4 = x + 8

2x - x = 8 - 4

x = 4

Numerator = x = 4

Denominator = ( x + 3 ) = 4 + 3 = 7

Therefore , the fraction is 4 / 7

Verification :-

$\sf{( x + 2 ) / ( x + 8 ) = 1/2}$

$\sf{4 + 2 / 4 + 8 = 1/2}$

$\sf{6 / 12 = 1/2}$

$\sf{1/2 = 1/2}$

Hence verified !!

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