A villager buys a goat and a sheep together for Rs 14250. He sells the sheep at a profit of 10% and the goat at a loss of 20%, but sells both animals at the same selling price. What was the cost price of the cheaper animal?

Introduction / Context:
This problem involves two different animals bought together and sold under different profit and loss conditions, but at the same final selling price. Such a setup leads to a pair of equations in terms of cost prices. This question helps you practice forming and solving linear equations from worded profit and loss conditions, which is a common theme in aptitude tests.

Given Data / Assumptions:

• Total cost price of goat and sheep together is Rs 14250.
• The sheep is sold at 10% profit.
• The goat is sold at 20% loss.
• Both animals are sold at the same selling price.
• We need the cost price of the cheaper animal.

Concept / Approach:
Let the cost price of the goat be G and that of the sheep be S. Then G + S = 14250. Sheep is sold at 10% profit, so its selling price is 1.10 * S. Goat is sold at 20% loss, so its selling price is 0.80 * G. These selling prices are equal. From this equality and the total cost equation, we can solve for G and S. The smaller of the two is the cheaper animal's cost price.

Step-by-Step Solution:
Let cost price of goat = G and cost price of sheep = S.Total cost price: G + S = 14250. (Equation 1)Sheep is sold at 10% profit, so selling price of sheep = 1.10 * S.Goat is sold at 20% loss, so selling price of goat = 0.80 * G.Given both are sold at the same price, so 1.10 * S = 0.80 * G. (Equation 2)From Equation 2, G = (1.10 / 0.80) * S = (11 / 8) * S = 1.375 * S.Substitute in Equation 1: 1.375 * S + S = 14250.2.375 * S = 14250.S = 14250 / 2.375 = 6000.Therefore G = 14250 - 6000 = 8250.The cheaper animal is the sheep, costing Rs 6000.

Verification / Alternative check:
Check selling prices. Sheep CP = Rs 6000, sold at 10% profit, so SPsheep = 6000 * 1.10 = Rs 6600. Goat CP = Rs 8250, sold at 20% loss, so SPgoat = 8250 * 0.80 = Rs 6600. Both selling prices are equal and match the condition. Total cost price is 6000 + 8250 = Rs 14250, as given. Therefore the values are consistent and correct.

Why Other Options Are Wrong:
If the cheaper animal cost were Rs 6600, Rs 7500 or Rs 8250, the corresponding other animal cost would either not sum to Rs 14250 or would not yield equal selling prices when the given profit and loss percentages are applied. Only a cheaper animal cost price of Rs 6000 leads to a valid solution satisfying both equations simultaneously.

Common Pitfalls:
Some students mistakenly assume equal profits or equal losses instead of equal selling prices, or they forget which animal has profit and which has loss. Others may set up equations incorrectly by mixing profit and loss percentages on the wrong cost prices. Writing clear expressions for each selling price and then equating them is the safest way to solve such problems.

Final Answer:
The cost price of the cheaper animal (the sheep) was Rs 6000.