Final answer:
The man buys eggs at 3 for Rs.5 and sells them at 5 for Rs.12, resulting in a gain of Rs.11/15 per egg. To find out how many eggs he purchased with a total gain of Rs.143, divide the total gain by the gain per egg, which results in 195 eggs.
Step-by-step explanation:
The question involves performing calculations related to profit in a simple business transaction, which falls under the subject of Mathematics. Specifically, this is a problem involving proportional reasoning and arithmetic operations — the kind of problem one would encounter in high school algebra or arithmetic practice.
The man buys eggs at a rate of 3 for Rs.5, meaning each egg costs him Rs. 5/3. He sells them at a rate of 5 for Rs.12, meaning he sells each egg for Rs. 12/5. His gain per egg can be calculated as the selling price per egg minus the cost price per egg.
The gain for each egg is 12/5 - 5/3. If we make the denominators the same, we have a common denominator of 15, making the gain (36/15 - 25/15) = 11/15 per egg. With a total gain of Rs.143 and a gain of Rs.11/15 per egg, we can divide the total gain by the gain per egg to find the number of eggs. Therefore, 143 ÷ (11/15) gives us the number of eggs, which, upon calculation, results in 195.