Question

The numerator and 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

Let the fraction be x/y.

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

=> x/y=3/2

=> x = (3y/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.

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

Substitute x with using the new equation to form one equation with only one variable. Solve for that equation.

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

=> (1.5y + 3)/(y - 2) = 2.25

=> y = 10

Plug x in (1).

=> x = (3y/2)

=> x = 15

Hence, the fraction is 15/10 = 3/2.

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