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 1/5Find the rational number.

ANS=let the numerator=x
so, x/x+7 is the original
rational number. Adding 2 to denominator and subtracting 3 from x-3/x-9=1/5
Cross multiplying
5x-​

Answer 1

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 the denominator, the new rational number is ⅕. Find the rational number.

Answer

Let the numerator be x

Denominator = x + 7

Original Rational number $\sf = \frac{x}{x + 7}$

Subtracting 3 from numerator = x - 3

Adding 2 to denominator = x + 7 + 2 = x + 9

New rational number :-

$\sf \frac{x - 3}{x + 9} = \frac{1}{5}$

$\sf = 5x - 3 = x + 9$

$\sf = 5x - x = 9 + 3$

$\sf = 4x = 12$

$\sf = x = \frac{12}{4}$

$\sf = x = 3$

Answer 2

Given :

• 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 :

• The Rational Number .

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 new number becomes 1/5 .

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

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

A.T.Q :

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

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

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

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

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

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

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

Value of x is 6 ..

Therefore :

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

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

$\longmapsto\tt\bf{15}$

So , The Rational Number is 6/15 ..