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
The current net monthly profit \(=$20 * 100 =$2000\).
$20 constitutes 10% of the item's price to the retailer.
It implies 20 = 10/100 * retail price of the item
The retail price of one item = \(\frac{(20*100)}{10}= 200\).
The selling price of one item \(=$200 + \text{ (profit on each item) }=$220\).
Discount is 5%. There fore New Selling price is 95% of $220
After Discount, new selling price of one item \(=$220 * 0.95 =$209\).
The new profit on each item \(=$209 -$200 =$9\).
Let the no of items retailer would sell at discounted price be \(x\).
The new net monthly profit \(= x *$9\)
The question is what must be \(x\) so that the new net monthly profit would exceed or equal the current net monthly profit.
\(x *$9 >= $2000\)
\(x >= 2000/9\).
\(x>= 222.222\)
Because \(x\) is number of item, hence it must be an integer. Nearest value \(x\) is 223.
Answer: D
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