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​

Answer 1

Step-by-step explanation:

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Answer 2

Solution

Given :-

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

• 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4.

Find :-

• Original fraction

Explanation

Let,

• Numerator be = x
• Denominator be = y

Case 1.

==> x : y = 3:2

==> x/y = 3/2

==> 2x - 3y = 0_________(1)

Case 2.

==> (x+3)(/(y-2) = 9/4

==> 4×(x+3) = 9×(y-2)

==> 4x - 9y = -18 + 12

==> 4x - 9y = -4 ________(2)

Multiply by 2 in equ(1)

==> 4x - 6y = 0_________(3)

Sub equ(2) & equ(3)

==> -9y + 6y = -4

==> 3y = 4

==> y = 4/3

Keep in equ(3)

==> 4x - 6×4/3 = 0

==> 4x = 8

==> x = 8/4

==> x = 2

Hence

• Fraction will be (x/y) = 2/(4/3) = 3/2