A is greater than B by 25% then by what percentage B is less than A? 
Q. $A$ is greater than $B$ by $25\text{%}$ then by what percentage $B$ is less than $A$ ?

my approach:
$A$ is greater than $B$ by $25$% then
$${A-B\over B}\times 100=25$$
$$A=B+0.25B=1.25B$$
Now, $B$ is less than $A$ by %
$$\frac{A-B}{B}\times 100=\frac{1.25B-B}{B}\times100=25\text{%}$$
Is my answer correct? I don't know where I am wrong.
Help me solve this question. Thanks.
 A: Your answer is not correct. You must take $\text{%}$ of B w.r.t. A as follows
$$\frac{A-B}{A}\times 100=\frac{1.25B-B}{1.25B}\times 100=\frac{1}{5}\times 100=20\text{%}$$
A: There's a problem in your question. In Q   you say

$A$ is greater than $B$ by $20\%$

but then in your attempt you say

$A$ is greater than $B$ by $25\%$.

I will assume the second statement is correct.
I think the best way to think of percentage change is as multiplication by a factor. Then
"$A$ is greater than $B$ by $25\%$" means
$$
A = 1.25B .
$$
So (solving for $B$)
$$ B= \frac{A}{1.25}=  \frac{1}{1.25}A = 0.8A = (1-0.2)A
$$
so $B$ is $20\%$ less than $A$.
For a slightly more abstract argument, see
How to get the reverse percentage (not amount of reverse percentage)?
A: In such questions is most important to clearing which number we are taking as 100%.
When we say $A$ is greater than $B$ by 25% of $B$ then $A=B+B\cdot 0.25$
When we say $A$ is greater than $B$ by 25% of $A$ then $A=B+A\cdot 0.25$
Same for reverse.
A: Working with percentages is always, always, always a multiplication, never, never, never and addition or a subtraction, like in this case:
A = 1.25 * B
B = 1/1.25 * A
  = 0.8 * A

And 0.8*... means, subtract 20%.
