A man buys two horses for ₹ 1,350. He sells one so as to loss 6% and the others so as to gain 7.5%. On the whole he neither gains nor losses. The cost of each horse is :

Question

Accepted Answer

To determine why Option 4 is the correct answer, let's analyze the problem and perform the necessary calculations.

The man buys two horses for a total of ₹ 1,350. Let's denote the cost price of the first horse as ₹ x and the second horse as ₹ y. Therefore, we have:

$$ x + y = 1350 $$

He sells the first horse at a 6% loss and the second horse at a 7.5% gain. Since he neither gains nor loses overall, the total selling price of both horses must equal the total cost price of ₹ 1,350.

1. **First Horse:**
   - Cost Price = ₹ x
   - Selling Price at 6% loss = $ x - \frac{6}{100} \times x = 0.94x $

2. **Second Horse:**
   - Cost Price = ₹ y
   - Selling Price at 7.5% gain = $ y + \frac{7.5}{100} \times y = 1.075y $

The total selling price of both horses is:

$$ 0.94x + 1.075y = 1350 $$

Now, we have two equations:
1. $ x + y = 1350 $
2. $ 0.94x + 1.075y = 1350 $

Let's solve these equations to find the values of x and y.

From equation 1, express y in terms of x:

$$ y = 1350 - x $$

Substitute this into equation 2:

$$ 0.94x + 1.075(1350 - x) = 1350 $$

Expanding and simplifying:

$$ 0.94x + 1451.25 - 1.075x = 1350 $$

$$ -0.135x + 1451.25 = 1350 $$

$$ -0.135x = 1350 - 1451.25 $$

$$ -0.135x = -101.25 $$

$$ x = \frac{-101.25}{-0.135} $$

$$ x = 750 $$

Now, substitute x = 750 back into the equation for y:

$$ y = 1350 - 750 $$

$$ y = 600 $$

Thus, the cost of the first horse is ₹ 750 and the cost of the second horse is ₹ 600, which corresponds to Option 4: ₹ 750; ₹ 600.

**Explanation for Other Options:**

1. **Option 1: ₹ 570; ₹ 600**
   - If x = 570 and y = 600, then x + y = 1170, which does not satisfy the condition x + y = 1350.

2. **Option 2: ₹ 750; ₹ 606**
   - If x = 750 and y = 606, then x + y = 1356, which exceeds the total cost of ₹ 1350.

3. **Option 3: ₹ 705; ₹ 660**
   - If x = 705 and y = 660, then x + y = 1365, which also exceeds the total cost of ₹ 1350.

Therefore, Option 4 is the only choice that satisfies all the conditions of the problem, making it the correct answer.