Question

the denominator of a rational number is greater than its numerator by 3 if 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1 / 5 find the original number

Answer 1

Let,

Numerator be x
Denominator be (x +3)

Fraction = x/(x+3)

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According to the question,

$\frac{x - 3}{x + 3 + 2} = \frac{1}{5}$

$\frac{x - 3}{x + 5} = \frac{1}{5} \\ \\ 5(x - 3) = 1(x + 5) \\ \\ 5x - 15 = x + 5 \\ \\ 5x - x = 5 + 15 \\ \\ 4x = 20 \\ \\ x = \frac{20}{4} \\ \\ x = 5$



Then,

$fraction = \frac{5}{5 + 3} = \frac{5}{8}$




I hope this will help you


-by ABHAY

Answer 2

Let the numerator be x. Then,
denominator of the rational number = x + 7
Therefore, the rational number = x/x+7
It is given that if 3 is subtracted from the numerator and 2 is added to its denominator, then new number becomes 1/5.

Therefore, x-3/(x+7)+2 = 1/5

=> x-3/x+9 = 1/5
=> 5x - 15 = x+9
=> 5x-x = 9+15
=> 4x = 24
=> x = 24/4 = 6

Putting x = 6 in (1), we get
Required rational number = 6/6+7 = 6/13