A trader has 27 watches at the start and after selling some he reduces price by $5. He sells them all for $475?

Question

A market trader has 27 watches at the start of the day and after selling some he reduces the price by $5. He sells them all for $475. What was the original price?

Answer 1

Price of the watch should be greater than 475/27 = { average price of the watch } = 17.5926
This is because
(Watch Price) > (Average Watch Price) > (Watch Price - $5).
also
we know that
X*Y + (X-5)*(27-Y) = 475
where
X => Price of the watch
Y => Watches that were sold for X
Since Y cannot be a fraction we can use this fact to our advantage
If we assume X = 18 then Y = 24.8 ===> implies X not equal to 18
If we assume X = 19 then Y = 19.4 ===> implies X not equal to 19
If we assume X = 20 then Y = 14 ===> implies X is equal to 20

Now 20*14 + (20-5)*(27-14) = 475 or in other words he sold the first 14 watches for $20 and then the remaining 13 watches were sold for $15.