A villager buys a goat and a sheep together for Rs.14,250. 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?
Question
A villager buys a goat and a sheep together for Rs.14,250. 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?
Solution
Let's solve this step by step:
Step 1: Let's assume the cost price of the sheep is 'S' and the cost price of the goat is 'G'. According to the problem, S + G = Rs.14,250.
Step 2: The sheep was sold at a profit of 10%, which means it was sold for 110% of its cost price. Similarly, the goat was sold at a loss of 20%, which means it was sold for 80% of its cost price.
Step 3: According to the problem, the selling price of the sheep and the goat was the same. So, 110% of S = 80% of G.
Step 4: Solving this equation, we get S/G = 8/11.
Step 5: Now we have two equations (S + G = Rs.14,250 and S/G = 8/11) and two unknowns (S and G). We can solve these equations simultaneously to find the values of S and G.
Step 6: Solving these equations, we get S = Rs.5500 and G = Rs.8750.
Step 7: Therefore, the cost price of the cheaper animal (the sheep) is Rs.5500.
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