SOLUTION: If discount is 10% then loss is 16% find loss% if discount becomes 25%?

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.

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