A man buys 5 horses and 7 oxen for Rs 5850. He sells the horses at a profit of 10% and oxen at a profit of 16% and his whole gain is Rs 711. What price does he pay for a horse?

Answer

To solve the problem step by step, we will follow the information provided in the question and use the concepts of profit and loss.

### Step 1: Understand the Total Cost Price
The man buys 5 horses and 7 oxen for a total of Rs 5850.

### Step 2: Calculate Total Profit Percentage
The total profit made by the man is Rs 711. To find the total 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:
\[ \text{Profit Percentage} = \left( \frac{711}{5850} \right) \times 100 \]

### Step 3: Simplify the Profit Percentage Calculation
Calculating the above expression:
\[ \text{Profit Percentage} = \left( \frac{711 \times 100}{5850} \right) = \frac{71100}{5850} \approx 12.15\% \]

### Step 4: Set Up the Profit Percentages for Horses and Oxen
The horses are sold at a profit of 10% and the oxen at a profit of 16%. We now have:
- Profit percentage of horses = 10%
- Profit percentage of oxen = 16%
- Overall profit percentage = 12.15%

### Step 5: Use Alligation to Find the Ratio of Cost Prices
Using the method of alligation to find the ratio of the cost prices of horses and oxen:
- Difference between overall profit and horse profit: \(12.15 - 10 = 2.15\)
- Difference between oxen profit and overall profit: \(16 - 12.15 = 3.85\)

### Step 6: Remove Decimals and Find the Ratio
To simplify, we can remove the decimals:
- Convert \(2.15\) to \(215\)
- Convert \(3.85\) to \(385\)

Now, we can find the ratio:
\[ \text{Ratio} = \frac{215}{385} \]
Dividing both by 5 gives:
\[ \text{Ratio} = \frac{43}{77} \]

### Step 7: Total Parts and Cost Price Calculation
The total parts in the ratio is \(43 + 77 = 120\). This means:
\[ 120 \text{ parts} = 5850 \text{ Rs} \]
Thus, the value of one part is:
\[ \text{Value of one part} = \frac{5850}{120} = 48.75 \text{ Rs} \]

### Step 8: Calculate Total Cost Price of Horses
Now, we can find the total cost price of the horses:
\[ \text{Total CP of Horses} = 77 \times 48.75 = 3753.75 \text{ Rs} \]

### Step 9: Calculate Cost Price of One Horse
Finally, to find the cost price of one horse:
\[ \text{Cost Price of One Horse} = \frac{3753.75}{5} = 750.75 \text{ Rs} \]

### Final Answer
The price paid for one horse is Rs 750.75.

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