Question

The numerator and the denominator of a fraction are in the ratio 3:2. I 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is Find the original fraction​

Answer 1

The numerator and the denominator of a fraction are in the ratio 3:2.

Assume that the number is 3x and denominator be 2x.

Also said that, if 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed.

As per given condition,

→ (3x + 3)/(2x - 2) = 9/4

→ 4(3x + 3) = 9(2x - 2)

→ 12x + 12 = 18x - 18

→ 6x = 30

→ x = 5

Therefore,

Numerator = 3x = 3(5) = 15

Denominator = 2x = 2(5) = 10

Hence, the fraction is 15/10.

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Answer 2

❣Answer❣

Let the numerator be x and denominator be y.

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

According to the question :

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

$4x + 12 = 9y - 18$

$4x + 30 = 9y$

substitute the value of x in terms of y

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

$6y + 30 = 9y$

$3y = 30$

$y = \frac{30}{3}$

$y = 10$

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

Therefore fraction is :-

$\frac{15}{10}$

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