denominator of a fraction is 1 more than its numerator. the fraction reduces to one fourth when numerator is reduced by 2 and denominator is increased by 3. find the number

Oriningal fraction ---- x/(x+1)

new result:

(x-2)/(x+4) = 1/4
cross-multiply
4x - 8 = x+4
3x = 12
x = 4

original fraction ----- 4/5

check:
new fraction :
(4-2)/(5+3) = 2/8
which is 1/4

To solve this problem, we can start by assigning variables to the unknown quantities. Let's say the numerator of the fraction is represented by 'x', and the denominator is represented by 'x + 1' because the denominator is 1 more than the numerator.

According to the problem, the fraction reduces to one-fourth when the numerator is reduced by 2 and the denominator is increased by 3. This can be expressed as:

(x - 2) / (x + 1 + 3) = 1/4

Simplifying the equation, we get:

(x - 2) / (x + 4) = 1/4

Now, we can cross multiply to solve for 'x':

4(x - 2) = (x + 4) * 1

4x - 8 = x + 4

4x - x = 4 + 8

3x = 12

x = 12 / 3

x = 4

Therefore, the numerator of the fraction is 4, and the denominator is (4 + 1) = 5.