NandishSS wrote:Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
A. 191
B. 213
C. 221
D. 223
E. 226
Since he sells 100 items and each item has a profit of $20, he makes a total profit of 100 x 20 = 2000 dollars a month. Furthermore, Since $20 constitutes 10% of the item's price to the retailer, the cost of each item when the retailer purchases it is 20/0.1 = 200 dollars and thus the price of each item when he sells it = 200 + 20 = 220 dollars.
Now he plans to discount the selling price by 5%; thus, each item would be sold for 220 x 0.95 = 209 dollars.
We can let n = the total number of items he has to sell now to still make the $2000 monthly profit.
R - C = P
209n - 200n = 2000
9n = 2000
n = 222.22
Since n has to be an integer, he has to sell at least 223 items. (Note: Selling 222 items will be just short of making the $2000 profit, but selling 223 items will do.)
Answer:
D
