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A is greater than B by 25% then by what percentage B is less than A?

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

my approach:

$A$ is greater than $B$ by $25$% then

$${A-Bover B}times 100=25$$

$$A=B+0.25B=1.25B$$

Now, $B$ is less than $A$ by %

$$frac{A-B}{B}times 100=frac{1.25B-B}{B}times100=25text{%}$$

Is my answer correct? I don’t know where I am wrong.

Help me solve this question. Thanks.

Mathematics Asked by user809080 on December 3, 2021

4 Answers

4 Answers

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%.

Answered by Dominique on December 3, 2021

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)?

Answered by Ethan Bolker on December 3, 2021

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 $A=B+Bcdot 0.25$

When we say $A$ is greater than $B$ by 25% of $A$ then $A=B+Acdot 0.25$

Same for reverse.

Answered by zkutch on December 3, 2021

Your answer is not correct. You must take $text{%}$ of B w.r.t. A as follows $$frac{A-B}{A}times 100=frac{1.25B-B}{1.25B}times 100=frac{1}{5}times 100=20text{%}$$

Answered by Harish Chandra Rajpoot on December 3, 2021

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