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 15 4 is formed. Find the original fraction.

original fraction ----- 5x/2x

new fraction: (5x+5)/(2x-2)

I can't make out what 15 4 is supposed to be.
Once you have decided, set that equal to
(5x+5)/(2x-2) , looks like you would just cross-multiply to solve

To find the original fraction, let's assume the numerator is 5x and the denominator is 2x (since the numerator and denominator are in a ratio of 5:2).

According to the problem, when 5 is added to the numerator and 2 is subtracted from the denominator, a new fraction of 15/4 is formed.

So we can set up the equation:
(5x + 5) / (2x - 2) = 15/4

Next, we can cross-multiply to simplify the equation:
4(5x + 5) = 15(2x - 2)

Expand the equation:
20x + 20 = 30x - 30

Now, let's isolate the variable by moving all the x terms to one side and the constant terms to the other side:
20x - 30x = -30 - 20
-10x = -50

Divide both sides of the equation by -10 to solve for x:
x = -50 / -10
x = 5

Now we know that x = 5, so we can substitute this value back into our assumption of the numerator and denominator:
Numerator = 5x = 5 * 5 = 25
Denominator = 2x = 2 * 5 = 10

Therefore, the original fraction is 25/10, which can be simplified to 5/2.

To solve this problem, let's break it down into steps:

Step 1: Write equations based on the given information.
Let the numerator and denominator of the original fraction be 5x and 2x respectively. We know that 5 is added to the numerator, so the new numerator is 5x + 5. Similarly, 2 is subtracted from the denominator, so the new denominator is 2x - 2. The new fraction formed is 15/4.

Step 2: Set up an equation using the given information.
Based on the equation, we can write:

(5x + 5)/(2x - 2) = 15/4

Step 3: Now we solve for x.
To solve this equation, we can cross-multiply:

4(5x + 5) = 15(2x - 2)
20x + 20 = 30x - 30

Simplifying the equation gives:
10x = 50
x = 5

Step 4: Find the original fraction.
Now that we know the value of x, we can substitute it back into our original fraction. The numerator is 5x, so the numerator of the original fraction is 5 * 5 = 25. The denominator is 2x, so the denominator of the original fraction is 2 * 5 = 10.

Therefore, the original fraction is 25/10, which can be simplified to 5/2.

So, the original fraction is 5/2.