. 2. A villager buys a goat and a sheep together for Rs. 14250. He sold the sheep at a profit of 10% and the goat at a loss of 20%. If he sold both the animals at the same price, then what was the cost price of the cheaper animal?

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Let's solve this profit and loss problem step by step. A villager buys a goat and a sheep together for fourteen thousand two hundred fifty rupees. The sheep is sold at a ten percent profit, while the goat is sold at a twenty percent loss. Both animals are sold at the same price. We need to find the cost price of the cheaper animal. Now let's set up our variables and equations. Let C s be the cost price of the sheep and C g be the cost price of the goat. We know that C s plus C g equals fourteen thousand two hundred fifty. The sheep is sold at ten percent profit, so its selling price is one point one zero times C s. The goat is sold at twenty percent loss, so its selling price is zero point eight zero times C g. Since both animals are sold at the same price, we have one point one zero C s equals zero point eight zero C g. Now let's solve the system of equations. From the condition that both animals are sold at the same price, we have one point one zero C s equals zero point eight zero C g. We can rewrite this as C s over C g equals zero point eight over one point one zero, which simplifies to eight over eleven. This gives us eleven C s equals eight C g. Now we have our system: C s plus C g equals fourteen thousand two hundred fifty, and eleven C s equals eight C g. From the second equation, we can express C g in terms of C s as C g equals eleven over eight times C s. Now let's substitute and solve. We substitute C g equals eleven over eight C s into the first equation: C s plus eleven over eight C s equals fourteen thousand two hundred fifty. Combining the terms, we get nineteen over eight C s equals fourteen thousand two hundred fifty. Solving for C s: C s equals fourteen thousand two hundred fifty times eight divided by nineteen, which equals one hundred fourteen thousand divided by nineteen, giving us C s equals six thousand. Then C g equals fourteen thousand two hundred fifty minus six thousand, which equals eight thousand two hundred fifty. The sheep costs six thousand rupees and the goat costs eight thousand two hundred fifty rupees. Therefore, the cheaper animal is the sheep. To summarize our solution: We defined variables for the cost prices of both animals, used the profit and loss conditions along with the equal selling price constraint to create a system of equations. Solving this system, we found that the sheep costs six thousand rupees and the goat costs eight thousand two hundred fifty rupees. Therefore, the cost price of the cheaper animal is six thousand rupees.