Question

The numerator of a fraction is 3 less than the denominator. If 1 is added to both its numerator and
1
denominator, it becomes Find the fraction.
2
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3
3​

Answer 1

Correct Question :

The numerator of a fraction is 3 less than the denominator. If 1 is added to both its numerator and denominator, it becomes 2/3 Find the fraction.

Given :

• The numerator of a fraction is 3 less than the denominator.
• If 1 is added to both its numerator and denominator, it becomes 2/3 .

To Find :

• Original Fraction .

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that Numerator of a fraction is less than its Denominator by 3 . So ,

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

Now ,

• If 1 is added to both its numerator and denominator, it becomes 2/3 .

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

$\longmapsto\tt{Denominator=x+1}$

A.T.Q :

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

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

$\longmapsto\tt{3x-6=2x+2}$

$\longmapsto\tt{3x-2x=2+6}$

$\longmapsto\tt\bf{x=8}$

Value of x is 8 .

Therefore :

$\longmapsto\tt{Numerator=8-3}$

$\longmapsto\tt\bf{5}$

$\longmapsto\tt{Denominator=x}$

$\longmapsto\tt\bf{8}$

So , The Fraction is 5/8 .

Answer 2

Answer:

5/8

Explanation:

Let denominator as 'x'

then,

x-3/x

If we add 1 for both denominator and numerator

x-3+1/x+1 = 2/3

By cross multiplication

(x-2)3 = (x+1)2

3x-6 = 2x+2

x = 8