If HCF (225,60) = 225 times 5 - 10x, then find the value of x.

We are given the equation:
HCF(225, 60) = 225 * 5 - 10x.

Step 1: Find the HCF of 225 and 60
To find the HCF of 225 and 60, we can use the prime factorization method.

Prime factorization of 225:
225 = 3 * 3 * 5 * 5.

Prime factorization of 60:
60 = 2 * 2 * 3 * 5.

The common factors between 225 and 60 are 3 and 5. So,
HCF(225, 60) = 3 * 5 = 15.

Step 2: Substitute the value of HCF in the equation
Now, substitute the value of HCF(225, 60) = 15 into the equation:
15 = 225 * 5 - 10x.

Step 3: Solve for x
First, calculate 225 * 5:
225 * 5 = 1125.

Now the equation becomes:
15 = 1125 - 10x.

Next, subtract 1125 from both sides of the equation:
15 - 1125 = -10x,
-1110 = -10x.

Finally, divide both sides by -10 to solve for x:
x = -1110 / -10 = 111.

Final Answer:
The value of x is 111.