If 2 is added to the numerator of a fraction, it reduces to 1/2 and if

1.	If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3 . Find the fraction.
Answer» Let us consider, a fraction x/y, where x is numerator and y is denominator. As per the statement, (x + 2)/y = ½ x/y – 1 = 1/3 2x + 4 = y …(1) And, 3x = y – 1 …(2) Using Substitution method: Using (1) in (2) 3x = 2x + 4 – 1 3x = 2x + 3 x = 3 Form (1): y = 2(3) + 4 = 10 Answer: Required fraction is 3/10

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3 . Find the fraction.

Answer»

Let us consider, a fraction x/y, where x is numerator and y is denominator.

As per the statement,

(x + 2)/y = ½

x/y – 1 = 1/3

2x + 4 = y …(1)

And, 3x = y – 1 …(2)

Using Substitution method:

Using (1) in (2)

3x = 2x + 4 – 1

3x = 2x + 3

x = 3

Form (1): y = 2(3) + 4 = 10

Answer: Required fraction is 3/10