A man bought 5 horses and 7 cow's of Rs 5,850. If he gains 10% profit on horses selling and 16% profit after selling the cows. If he gains Rs 702, then find the cost price of each horse .

Options

A. Rs 720
B. Rs 780
C. RS 700
D. Rs 730

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the total cost price
The total cost price of 5 horses and 7 cows is given as Rs. 5,850.

### Step 2: Calculate the total profit
The total profit earned from selling both horses and cows is Rs. 702.

### Step 3: Calculate the overall profit percentage
To find the overall profit percentage, we can use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Total Profit}}{\text{Total Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{702}{5850} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \left( 0.12 \right) \times 100 = 12\% \]

### Step 4: Determine the profit percentages of horses and cows
The profit percentage on horses is 10%, and on cows, it is 16%.

### Step 5: Set up the ratio of cost prices
Let the cost price of horses be \( H \) and the cost price of cows be \( C \). We know:
\[ H + C = 5850 \]
The profit from horses is:
\[ \text{Profit from Horses} = 0.10H \]
The profit from cows is:
\[ \text{Profit from Cows} = 0.16C \]
The total profit is:
\[ 0.10H + 0.16C = 702 \]

### Step 6: Solve the equations
We have two equations:
1. \( H + C = 5850 \)
2. \( 0.10H + 0.16C = 702 \)

From the first equation, we can express \( C \) in terms of \( H \):
\[ C = 5850 - H \]
Substituting this into the second equation:
\[ 0.10H + 0.16(5850 - H) = 702 \]
Expanding this gives:
\[ 0.10H + 936 - 0.16H = 702 \]
Combining like terms:
\[ -0.06H + 936 = 702 \]
Subtracting 936 from both sides:
\[ -0.06H = 702 - 936 \]
\[ -0.06H = -234 \]
Dividing by -0.06:
\[ H = \frac{234}{0.06} = 3900 \]

### Step 7: Find the cost price of each horse
Since the cost price of 5 horses is \( H = 3900 \), the cost price of each horse is:
\[ \text{Cost Price of Each Horse} = \frac{3900}{5} = 780 \]

### Final Answer
The cost price of each horse is Rs. 780.

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