Question

the denominator of a ratio no. is greater than its numerator by 3, if 2 is added to the numerator and 3 is added to the denominator, then the number become 1/2 , find the original number​

Answer 1

Let the numerator of fraction be x

Denominator be y.

According to the question,

y = x + 3 ------ (Equation. 1)

$\sf{ \frac{x + 2}{y + 3} = \frac{1}{2} } \\ \\ \implies \sf 2(x + 2) = y + 3 \\ \implies \sf 2x + 4 = y + 3 \\ \implies \sf 2x - y = 3 - 4 \\ \implies \sf{2x - y = -1} \\ \implies \sf{y = 2x + 1}$

Equating values of y,

x + 3 = 2x + 1

=> 3 - 1 = 2x - x

=> x = 2

Now substitute value of x in any 1 of the equation.

y = x + 3

y = 2 + 3

y = 5

the original number is ²/₅