A person purchased 3 cows and 8 goats for Rs 47200 If he had purchased 8 cows and 3 gots then he would have to give Rs 53000 more . Find cost price of each cow.

Answer

To find the cost price of each cow, we can set up the problem using algebra. Let's denote the cost price of each cow as \( C \) and the cost price of each goat as \( G \).

### Step 1: Set up the equations based on the information given.
From the problem, we have two scenarios:

1. The cost of 3 cows and 8 goats is Rs. 47,200.
\[ 3C + 8G = 47200 \quad \text{(Equation 1)} \]

2. The cost of 8 cows and 3 goats is Rs. 53,000 more than the first scenario, which means:
\[ 8C + 3G = 47200 + 53000 = 100200 \quad \text{(Equation 2)} \]

### Step 2: Solve the equations.
Now we have two equations:
1. \( 3C + 8G = 47200 \)
2. \( 8C + 3G = 100200 \)

We can solve these equations simultaneously.

### Step 3: Multiply the first equation to align coefficients.
To eliminate \( G \), we can multiply Equation 1 by 3 and Equation 2 by 8:
\[ 9C + 24G = 141600 \quad \text{(Equation 3)} \]
\[ 64C + 24G = 801600 \quad \text{(Equation 4)} \]

### Step 4: Subtract the equations to eliminate \( G \).
Now, we subtract Equation 3 from Equation 4:
\[ (64C + 24G) - (9C + 24G) = 801600 - 141600 \]
This simplifies to:
\[ 55C = 660000 \]

### Step 5: Solve for \( C \).
Now, divide both sides by 55:
\[ C = \frac{660000}{55} = 12000 \]

### Conclusion:
The cost price of each cow is Rs. 12,000.

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