Question 1062839: If discount is 10% then loss is 16% find loss% if discount becomes 25%?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
i think the answer will be 30% based on some other reasoning that i will detail later.
to see if this is correct, i'll use assumed numbers to see what comes out.
i'll assume the cost is 100.
if it was sold at a 16% loss, then the sale price had to be 84.
if it was sold at a 10% discount, then the retail price had to be 93 and 1/3.
this is equivalent to a retail price of 280/3.
now, if sale price is 75% of the retail price, then sale price is equal to .75 * 280/3 = 70
cost is still the same at 100.
loss is now 100 - 70 = 30
30/100 is equal to 30% of the cost.
this confirms the solution is correct.
this should be able to be done with variables instead of number.
let C = cost.
let R = retail price
let S = sale price
with a 10% discount, you get S = R - .10 * R = .9 * R.
with a 16% loss, you get S = C - .16 * C = .84 * C
we have S = .9 * R and we have S = .84 * C
this means that .9 * R = .84 * C
we can solve for C to get C = .9 * r / .84
if we change the discount to 25%, then we get S = .75 * R
because of this change, S = .84 * C will becomes some other value times C which we don't know yet.
we'll make S = x * C
we will get:
S = .75 * R
S = x * C
since they're both equal to S, we get .75 * R = x * C
we solve for C to get C = .75 * R / x
previously we had C = .9 * R / .84
since they're both equal to C, we get .75 * R / x = .9 * R / .84
we cross multiply to get .75 * R * .84 = .9 * R * x
we solve for x to get x = (.75 * R * .84) / (.9 * R) = .7
this means that S = .7 * C
since L = (C - S) / C, we get L = (C - .7 * C) / C which gets L = .3 * C / C which gets L = .3 = 30%.
this says that you sold at a 30% loss.
30% should be your answer.
|
|
|
