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?

Options

A. 8250
B. 6600
C. 7500
D. 6000

Answer

To solve the problem step-by-step, we need to find the cost price of the cheaper animal (either the goat or the sheep) after understanding the transactions involved.

### Step 1: Define Variables
Let the cost price of the goat be \( G \) and the cost price of the sheep be \( S \). According to the problem, we have:
\[ G + S = 14,250 \]

### Step 2: Calculate Selling Prices
The sheep is sold at a profit of 10%. Therefore, the selling price (SP) of the sheep can be calculated as:
\[ SP_{sheep} = S + 0.10S = 1.10S \]

The goat is sold at a loss of 20%. Therefore, the selling price of the goat can be calculated as:
\[ SP_{goat} = G - 0.20G = 0.80G \]

### Step 3: Set Selling Prices Equal
Since both animals are sold at the same price, we can set their selling prices equal to each other:
\[ 1.10S = 0.80G \]

### Step 4: Express G in terms of S
From the equation \( 1.10S = 0.80G \), we can express \( G \) in terms of \( S \):
\[ G = \frac{1.10S}{0.80} = \frac{11S}{8} \]

### Step 5: Substitute G in the Total Cost Equation
Now, substitute \( G \) in the total cost equation \( G + S = 14,250 \):
\[ \frac{11S}{8} + S = 14,250 \]
To combine the terms, convert \( S \) to have a common denominator:
\[ \frac{11S}{8} + \frac{8S}{8} = 14,250 \]
\[ \frac{19S}{8} = 14,250 \]

### Step 6: Solve for S
Now, multiply both sides by 8 to eliminate the fraction:
\[ 19S = 14,250 \times 8 \]
\[ 19S = 114,000 \]
Now, divide both sides by 19:
\[ S = \frac{114,000}{19} = 6,000 \]

### Step 7: Find G
Now that we have \( S \), we can find \( G \):
\[ G = 14,250 - S = 14,250 - 6,000 = 8,250 \]

### Step 8: Identify the Cheaper Animal
Since \( S = 6,000 \) (the sheep) and \( G = 8,250 \) (the goat), the cheaper animal is the sheep.

### Conclusion
The cost price of the cheaper animal (the sheep) is:
\[ \text{Cost Price of the Cheaper Animal} = 6,000 \]

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