the numerator and the denominator of a fraction are in the ratio 3:2 if 3 is added to the - Maths - Basic Geometrical Ideas

Question

the numerator and the denominator of a
fraction are in the ratio 3:2 if 3 is added to the numerator and 2
is subtracted from the denominator, a new fraction is formed whose
value is 9/4 find the original fraction

Ajanta Trivedi · Accepted Answer

let the numerator be x and denominator be y.

$\frac{x}{y} = \frac{3}{2} \Rightarrow 2 x = 3 y$

according to the question:

$\frac{x + 3}{y - 2} = \frac{9}{4} 4 x + 12 = 9 y - 18 4 x + 30 = 9 y$

substitute the value of x in terms of y

$4 \times \frac{3}{2} y + 30 = 9 y 6 y + 30 = 9 y 3 y = 30 y = 10$

$x = \frac{3}{2} \times (10) = 15$

therefore fraction is $\frac{15}{10}$

the numerator and the denominator of a fraction are in the ratio 3:2. if 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4. find the original fraction.