The correct answer is option (E):
0.079
Let's break down this profit calculation step-by-step.
First, we need to calculate the cost price (CP) of each watch. The trader buys 240 watches for ` 50,400. Therefore, the CP of one watch is ` 50,400 / 240 = ` 210.
Next, we calculate the marked price (MP) of each watch, which is given as ` 320.
The trader offers a 15% discount on each watch. The discount amount is 15/100 * `320 = ` 48.
The selling price (SP) of each watch after the discount is `320 - `48 = ` 272.
The trader also gives 1 watch free for every 5 watches purchased. To maximize profit, we want to consider the minimum number of paid watches for all 240 watches the trader has. This means for every 6 watches (5 paid + 1 free), the customer effectively receives 6.
To determine how many sets of 6 watches are in 240, we divide 240 by 6: 240 / 6 = 40 sets.
So, the trader effectively sells 5 watches in each set of 6. This means 40 sets * 5 watches/set = 200 paid watches.
Now, we calculate the total revenue from selling 200 watches at ` 272 each. Total revenue = 200 * `272 = ` 54,400.
The total cost price for all 240 watches is ` 50,400.
The profit is the difference between the total revenue and the total cost price: ` 54,400 - ` 50,400 = ` 4,000.
The profit percentage is (Profit / Cost Price) * 100: (` 4,000 / ` 50,400) * 100 = 7.936%.
Rounding this to the nearest thousandth, the profit percentage is approximately 7.9%. Converting this to a decimal, we get 0.079. Therefore, the minimum possible overall percentage of profit is 0.079.