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 .

Answer 1

Let the numerator = x
So, x/x+7 is the original rational number.
Adding 2 to denominator and subtracting 3 from numerator
x - 3/ x + 9 = 1/5
Cross multiplying
5x - 15 = x + 9
4x = 24
x = 24/4
x = 6
Original rational number is
6/13
6/13 is the original rational number

Answer 2

Let the numerator of the fraction be x and the denominator of the fraction be ( x + 7 ) as it is 7 more than the numerator.

∴ Fraction = $\dfrac{x}{x+7}$

Given that if 3 is subtracted from the numerator and 2 is added to its denominator , the new number becomes 1/5

As numerator was x, 3 subtracted from numerator = ( x - 3 )

As denominator was x + 7 , 2 added to denominator = ( x + 7 + 2 )

                                                                                       = x + 9

New fraction =$\dfrac{x-3}{x+9}$

According to the question, new fraction is equal to 1 / 5.

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

x + 9 = 5( x - 3 )

x + 9 = 5x - 15

9 + 15 = 5x - x

24 = 4x

24 / 4 =  x

6 = x

Therefore the required fraction is $\dfrac{x}{x+7} =\dfrac{6}{6+7}=\dfrac{6}{13}$

Rational number = 6 / 13