Teenagers shoe company sells the shoes whose prices i.e., cost prices and selling prices are the multiples of either 13,14,15,16,17,18 or 19, starting from ₹ 399 to ₹ 699 `(i.e.,399 leCP//SPle699)` What can be the maximum profit of the company?

Options

A. ₹ 292
B. ₹ 398
C. ₹ 298
D. ₹ 300

Answer

To solve the problem of finding the maximum profit for the Teenagers Shoe Company, we need to identify the cost price (CP) and selling price (SP) that are multiples of the given numbers (13, 14, 15, 16, 17, 18, or 19) within the specified range of ₹399 to ₹699.

### Step-by-Step Solution:

1. **Identify the Cost Price (CP):**
- The cost price must be a multiple of either 13, 14, 15, 16, 17, 18, or 19 and should be at least ₹399.
- Check if ₹399 is a multiple of any of these numbers:
- 399 ÷ 13 = 30.69 (not a multiple)
- 399 ÷ 14 = 28.5 (not a multiple)
- 399 ÷ 15 = 26.6 (not a multiple)
- 399 ÷ 16 = 24.94 (not a multiple)
- 399 ÷ 17 = 23.47 (not a multiple)
- 399 ÷ 18 = 22.17 (not a multiple)
- 399 ÷ 19 = 21 (is a multiple)
- Therefore, the cost price (CP) is **₹399**.

2. **Identify the Selling Price (SP):**
- The selling price must be a multiple of the same numbers and should not exceed ₹699.
- Start checking from the maximum possible selling price of ₹699 downwards:
- Check if ₹699 is a multiple of any of the numbers:
- 699 ÷ 13 = 53.77 (not a multiple)
- 699 ÷ 14 = 49.93 (not a multiple)
- 699 ÷ 15 = 46.6 (not a multiple)
- 699 ÷ 16 = 43.69 (not a multiple)
- 699 ÷ 17 = 41.12 (not a multiple)
- 699 ÷ 18 = 38.83 (not a multiple)
- 699 ÷ 19 = 36.79 (not a multiple)
- Since 699 is not a multiple, check lower values:
- The next multiples for each number:
- For 13: 13 x 53 = 689
- For 14: 14 x 49 = 686
- For 15: 15 x 46 = 690
- For 16: 16 x 43 = 688
- For 17: 17 x 40 = 680
- For 18: 18 x 37 = 666
- For 19: 19 x 36 = 684
- The closest valid multiple of 19 is **₹684**.

3. **Calculate the Maximum Profit:**
- Profit is calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
- Substitute the values:
\[ \text{Profit} = 684 - 399 = 285 \]

### Conclusion:
The maximum profit the Teenagers Shoe Company can achieve is **₹285**.