If 80% of A=20% of B and B=5x% of A, then the value of X is:

The correct answer is 80.

Step-by-Step Explanation:

Step 1: Translate the first given equation into a mathematical statement.
We are given that 80% of A is equal to 20% of B.
In mathematical terms, "percentage of" can be written as multiplication by a fraction over 100.

$\frac{80}{100}\times A=\frac{20}{100}\times B$

Step 2: Simplify the relation between A and B.
Multiply both sides of the equation by 100 to eliminate the denominators:

$80\times A=20\times B$

Now, express B in terms of A by dividing both sides by 20:

$B=\frac{80}{20}\times A$

$B=4\times A$

Step 3: Translate the second given equation and solve for x.
We are also given that B = 5x% of A.
Writing this percentage as a fraction:

$B=\frac{5x}{100}\times A$

Substitute $B=4A$ into this equation:

$4A=\frac{5x}{100}\times A$

Step 4: Solve for x.
Divide both sides by A (assuming A ≠ 0):

$4=\frac{5x}{100}$

Multiply both sides by 100:

$400=5x$

Divide by 5:

$x=\frac{400}{5}$

$x=80$

Thus, the value of x is 80.