To reduce a quantity by 25%, you need to take 100% of minus 25%.
By dividing by 125%, you're really reducing the quantity by 20%.
What is the difference, please explain..!!
A pair of shoes is normally priced at $37. What will be the sale price if a 25% sales discount is offered?
I would assume i reduce $37 by 25%, i.e 37/1.25 = $29.60
However the answer is $37 x 0.75 = $27.75.
What is the difference in arising to the two unique solutions?
That's a very neat way of reversing a 25% increase.
You probably learnt it long ago in a lesson that was all about the difference you're asking about here, i.e. the very big difference between reducing by 25% and reversing a 25% increase.
Funny thing is, reversing should be the trickier of the two, but you've 'over-learnt' it, and are applying it regardless, just like most people (before that lesson) try to reverse a 25% increase by reducing by 25%.
So you need to get back in touch with the more obvious intuition. I suggest the following.
Think of the $37 as a tower of 4 bricks. You've been asked to remove the top one.
What you tried was a way of removing a fifth brick placed on the top.
now this makes sense.
the reason i did 37/1.25 to reduce by 25% is due to my financial instruments class where we have to discount a bond value back to its present value.
i.e if the future value of a bond 1 year from now is $1000, and interest rates are currently 5% then the present value is the future value DISCOUNTED back to one period at the interest rate, being 1000/1.05.
thank you.
if anyone can offer any more clarification, it would be appreciated.
actually im still confused.
lets look at it this way:
increasing $1000 by 25% is 1000 x 1.25 = $1250
now if we reduce $1250 by 25% again, are you saying it is $1250 x 0.75 = $937.50, and not $1250/1.25 = $1000?
Because $1250/1.25 is an 20% reduction (1/1.25 = 0.8).
this is correct?
EDIT:
so lets say i do add that 5th brick, then if i take 25% of the 5 brick structure, i get ((37 x 0.75 = 27.75).
Using this brick logic, how would you interpret 37/1.25 = 29.6 then?
Yes! Totally.
Although you can't do this without sawing into one of the bricks. Embarking on a 25% reduction in the first place should tell you to look at the given amount as a tower of 4 not 5.
As removing one of 5 bricks.
Or as reducing by 20%.
Or as dividing by five quarters (which would reverse a multiplication by five quarters which is an increase by one quarter).