A shopkeeper bought two items for a total of ₹60,000. He sold one item with…

To solve this problem, we can use the method of allegation, which is a very efficient way to find the ratio of the cost prices of two items when their individual profit/loss percentages and the overall gain percentage are known.

Step-by-Step Analysis
Identify the profit/loss percentages:

Item 1 (Profit): +25%

Item 2 (Loss): -15%

Overall Gain: +4%

Apply the Allegation Method:
The allegation method allows us to find the ratio of the cost prices by taking the difference between the overall gain and the individual profit/loss percentages.

Difference 1 (between Item 2 and Overall): |4 - (-15)| = 4 + 15 = 19

Difference 2 (between Item 1 and Overall): |25 - 4| = 21

The ratio of the Cost Price of Item 1 to the Cost Price of Item 2 is therefore 19 : 21.

Divide the total cost:

Total cost = 60,000

Total parts in ratio = 19 + 21 = 40

Value of one part = 60,000 / 40 = 1,500

Cost Price of Item 1 (sold with profit) = 19 * 1,500 = 28,500

The cost price of the item sold with profit is 28,500, which corresponds to Option 4.