Final answer:
To find the overall gain or loss, one must calculate the cost prices of the cows based on the given sale prices and percentage changes. However, with equal percentages, there will be an overall loss because percentage losses have a greater impact than the same percentage gains.
Step-by-step explanation:
The question requires us to calculate the total gain or loss when a man sells two cows each for Rs.15,640, making a 15% gain on one and a 15% loss on the other. To solve this, let's denote the cost price of the first cow as C1 and the second cow as C2. A gain of 15% on the first cow would mean he sold it for 1.15C1 and a loss of 15% on the second cow would mean he sold it for 0.85C2. Both cows are sold for Rs.15,640 so we have two equations: 1.15C1 = 15,640 and 0.85C2 = 15,640. Solving these equations gives the cost price for each cow, which we can use to then calculate the overall gain or loss.
However, without solving these equations, we can also understand that since the percentage gain and loss are the same, the man will experience an overall loss because the percentage loss always has a greater impact on cost price than the same percentage gain does on a different cost price. This results from the math behind percentage changes.