Calculating Selling Price for Desired Profit

This problem involves finding a new selling price for an item to achieve a specific profit percentage, given the initial selling price and its corresponding profit.

Here's the breakdown:

• Initial Selling Price (SP1) = Rs. 22,000
• Initial Gain Percentage (Gain1) = 10%
• Desired Gain Percentage (Gain2) = 14%
• We need to find the New Selling Price (SP2).

Calculating the Cost Price (CP)

First, we need to determine the original cost price of the cow. The formula relating Selling Price (SP), Cost Price (CP), and Gain Percentage is:

$$ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) $$

To find the Cost Price, we can rearrange the formula:

$$ CP = \frac{SP}{1 + \frac{Gain\%}{100}} $$

Using the initial values:

$$ CP = \frac{22000}{1 + \frac{10}{100}} $$

$$ CP = \frac{22000}{1 + 0.10} $$

$$ CP = \frac{22000}{1.10} $$

$$ CP = 20000 $$

So, the Cost Price of the cow is Rs. 20,000.

Calculating the New Selling Price (SP2) for 14% Gain

Now that we have the Cost Price, we can calculate the new Selling Price required to achieve a 14% gain. We use the same formula, but this time solving for the new SP (SP2) with the desired gain percentage (Gain2):

$$ SP2 = CP \times \left(1 + \frac{Gain2\%}{100}\right) $$

Plugging in the values:

$$ SP2 = 20000 \times \left(1 + \frac{14}{100}\right) $$

$$ SP2 = 20000 \times (1 + 0.14) $$

$$ SP2 = 20000 \times 1.14 $$

$$ SP2 = 22800 $$

Therefore, the man should sell the cow for Rs. 22,800 to gain 14%.