Question

The numerator of a fraction is 3 less than the denominator. If the numerator and denominator are
both increased by 2, the new fraction becomes6/7
Find the original fraction.
​

Answer 1

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

• numerator is 3 less than the denominator.

• if two is added to both numerator and denominator the fraction becomes 6/7

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

• ✦ Original fraction.

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

Let the denominator be x

Then the numerator is x - 3

According to condition:-

If numerator and denominator Both are increased by 2 .

Then,

The numerator = (x - 3)+2

⠀⠀⠀⠀⠀⠀⠀⠀⠀➝ x -1

The denominator = x +2

According to question:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀➝ x -1/x+2 = 6/7

⠀⠀⠀⠀⠀⠀⠀⠀⠀➝(x -1) ×7 = 6(x+2)

⠀⠀⠀⠀⠀⠀⠀⠀⠀➝ 7x -7 = 6x +12

⠀⠀⠀⠀⠀⠀⠀⠀⠀➝ 7x - 6x = 12 +7

⠀⠀⠀⠀⠀⠀⠀⠀⠀➝ x = 19

So, the numerator (x- 3)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 19 -3

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 16

Denominator = 19

So,

The original fraction = 16/19

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