The numerator and denominator of a fraction are in ratio 5 : 2, if 5 is added to the numerator and 2 is subtracted from the denominator a new fraction ¹/4 is formed.Find the original fraction.
10/6
Your question does not make sense.
If the ratio of numerator and denominator is 5:2 = 2.5
is impossible increase the numerator and decrease the denominator and get the ratio 1:4
To solve this problem, let's start by assigning variables to the numerator and denominator of the original fraction. Let's say the numerator is 5x and the denominator is 2x, where x is a positive integer.
We know that if we add 5 to the numerator and subtract 2 from the denominator, we get a new fraction of 1/4. So the new fraction can be written as:
(5x + 5) / (2x - 2) = 1/4
To solve this equation, we can cross-multiply:
(5x + 5) * 4 = 1 * (2x - 2)
20x + 20 = 2x - 2
Next, we want to isolate the variable x. Let's move all terms with x to one side of the equation and move the constant terms to the other side:
20x - 2x = -2 - 20
18x = -22
Now, divide both sides of the equation by 18 to solve for x:
x = -22 / 18
Simplifying the right side gives:
x ≈ -1.222
Since we cannot have a negative numerator or denominator in a fraction, we can conclude that there is no valid solution for x.
Therefore, there is no original fraction that satisfies the given conditions.