Radheshyam bought a cow and a buffalo for his dairy. But he thought of selling them off due to some unforeseen circumstanc es. If he sells the cow at 10%. loss and the buffalo at 20% prof it, he will have no profit and no loss. But if he sells the cow at a profit of 5% and the buffalo at a loss of 15%, he would lose Ra 800 in the bargain. How much did Radheyshyam pay for the buffalo?

Options

A. 1.Rs.8000
B. 2.Rs.32000
C. 3.Rs.4000
D. 4.Rs.16000

Answer

To solve the problem step by step, we will define variables for the cost prices of the cow and the buffalo and set up equations based on the information given in the question.

### Step 1: Define Variables
Let:
- \( C \) = Cost price of the cow
- \( B \) = Cost price of the buffalo

### Step 2: Set Up the First Equation
According to the problem, if Radheshyam sells the cow at a 10% loss and the buffalo at a 20% profit, he will have no profit and no loss.

- Selling price of the cow at 10% loss = \( 0.9C \)
- Selling price of the buffalo at 20% profit = \( 1.2B \)

Since the total selling price equals the total cost price:
\[ 0.9C + 1.2B = C + B \]

### Step 3: Simplify the First Equation
Rearranging the equation:
\[ 0.9C + 1.2B = C + B \]
\[ 1.2B - B = C - 0.9C \]
\[ 0.2B = 0.1C \]
This simplifies to:
\[ 2B = C \quad \text{(Equation 1)} \]

### Step 4: Set Up the Second Equation
Now, if he sells the cow at a profit of 5% and the buffalo at a loss of 15%, he would lose Rs 800.

- Selling price of the cow at 5% profit = \( 1.05C \)
- Selling price of the buffalo at 15% loss = \( 0.85B \)

The total selling price in this case is:
\[ 1.05C + 0.85B = C + B - 800 \]

### Step 5: Simplify the Second Equation
Rearranging the equation:
\[ 1.05C + 0.85B = C + B - 800 \]
\[ 1.05C + 0.85B - C - B = -800 \]
\[ (1.05 - 1)C + (0.85 - 1)B = -800 \]
\[ 0.05C - 0.15B = -800 \]
This simplifies to:
\[ 5C - 15B = -8000 \quad \text{(Equation 2)} \]

### Step 6: Substitute Equation 1 into Equation 2
From Equation 1, we have \( C = 2B \). Substitute this into Equation 2:
\[ 5(2B) - 15B = -8000 \]
\[ 10B - 15B = -8000 \]
\[ -5B = -8000 \]
\[ B = 1600 \]

### Step 7: Find the Cost Price of the Buffalo
The cost price of the buffalo is:
\[ B = 1600 \]

### Final Answer
Radheshyam paid Rs 16,000 for the buffalo.

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