Decreasing b when a increases by 10%

[Jahnavi]

Homework Statement

a and B are two variables such that their
product ab = constant .If a increases by 10%,
by how much does b decrease ?

Homework Equations

The Attempt at a Solution

[/B]
ab = constant

If a changes to 11a/10 , then b has to change
to 10b/11.

% Change in b is = (b - 10b/11)/b = 9.09%

b decreases by 9.09% .

But the answer given is 10% .

Is 9.09% decrease in b correct ?

 

[I like Serena]

Hi Jahnavi,

Yep, 9.09% decrease in b is correct.

 

[Orodruin]

Yes.

By the same reasoning used to obtain the quoted answer you would get a 100% decrease in b if you increased a by 100%, which is ridiculous.