Question

The denominator of a rational number is greater than its numerator by 7. If 3
is subtracted from the numerator and 2 is added to its denominator, the new
1
number becomes . Find the rational number.
5​

Answer 1

Correct Question :

The denominator of a rational number is greater than its numerator by 7. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5 . Find the rational number.

Given :

• The denominator of a rational number is greater than its numerator by 7.
• If 3 is subtracted from the numerator and 2 is added to its denominator the fraction becomes 1/5 .

To Find :

• Original Fraction .

Solution :

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

As Given that Denominator of a rational number is greater than its numerator by 7 . So ,

$\longmapsto\tt{Denominator=x+7}$

Now ,

• If 3 is subtracted from the numerator and 2 is added to its denominator the fraction becomes 1/5 .

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

$\longmapsto\tt{Denominator=x+7+2=x+9}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-3}{x+9}=\dfrac{1}{5}}$

$\longmapsto\tt{5(x-3)=1(x+9)}$

$\longmapsto\tt{5x-15=1x+9}$

$\longmapsto\tt{5x-1x=9+15}$

$\longmapsto\tt\bf{4x=24}$

$\longmapsto\tt{x=\cancel\dfrac{24}{4}}$

$\longmapsto\tt\bf{x=6}$

Value of x is 6 .

Therefore :

$\longmapsto\tt{Numerator=x}$

$\longmapsto\tt\bf{6}$

$\longmapsto\tt{Denominator=6+7}$

$\longmapsto\tt\bf{13}$

So , The Fraction is 6/13 .

Answer 2

Given :-

The denominator of a rational number is greater than its numerator by 7. If 3

is subtracted from the numerator and 2 is added to its denominator, the new  number becomes 1/5

To Find :-

Rational number

Solution :-

Let the numerator be x

Denominator = Numerator + 7

Denominator = x + 7

When 3 subtracted from numerator

Numerator = x - 3

When 2 added to denominator

x - 3/x + 7 + 2 = 1/5

x - 3/x + 9 = 1/5

1(x + 9) = 5(x - 3)

x + 9 = 5x - 15

5x - x= 9 + 15

4x = 24

x = 24/4

x = 6

Now

Denominator = x + 7 = 6 + 7 = 13

Hence

Fraction = 6/13

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