SOLUTION: A watch is sold at a profit of 20% on the cost price after allowing a discount of 20% on the marked price. Find the M.P of the watch is a profit of Rs. 100 is made on it.

Question 1040589: A watch is sold at a profit of 20% on the cost price after allowing a discount of 20% on the marked price. Find the M.P of the watch is a profit of Rs. 100 is made on it.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let p = profit
let c = cost
let s = selling price
let m = markup price.

selling price is equal to 20% off of the markup price.
this means that s = m - .20 * m which becomes s = m * (1-.2) which becomes s = m*.80 which becomes s = .80 * m

so far you have s = .80 * m

you are given that p = 100.

so far you have:

p = 100
s = .80 * m

you are given that profit = 20% of cost.
this means that p = .20 * c
since p = 100, this means that 100 = .20 * c
divide both sides of this equation by .20 and solve for c to get c = 500.

so far you have:

p = 100
s = .80 * m
c = 500

since selling price is equal to cost plus profit, you get s = 500 + 100 = 600.

in the equation of s = .80 * m, replace s with 600 to get 600 = .80 * m.
divide both sides of this equation by .80 and solve for m to get m = 600 / .8 = 750

your markup price is 750.
you take 20% off of this to get a selling price of 600.
your profit is 100 which means your cost has to be 500.
a profit of 100 is equal to 20% of 500.

all requirements of the problem have been satisfied.

your solution is that the markup price is 750.
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