(d) What is the meaning of $$ 75 \% $$ loss? By selling an exhaust fan for Rs 1,470 , Mr. Ekaraj gains $$ \frac{1}{6} $$ of its cost price.

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To solve the problem, we need to determine the cost price of the exhaust fan based on the information provided.

### Known Conditions:
1. Selling Price (SP) = Rs 1,470
2. Gain = $$ \frac{1}{6} $$ of the Cost Price (CP)

### Step-by-Step Solution:

1. **Understanding Gain**:
   The gain is defined as the difference between the selling price and the cost price. Mathematically, this can be expressed as:
   $$
   \text{Gain} = \text{SP} - \text{CP}
   $$

2. **Expressing Gain in Terms of CP**:
   According to the problem, the gain is also given as $$ \frac{1}{6} $$ of the cost price:
   $$
   \text{Gain} = \frac{1}{6} \times \text{CP}
   $$

3. **Setting Up the Equation**:
   We can set the two expressions for gain equal to each other:
   $$
   \text{SP} - \text{CP} = \frac{1}{6} \times \text{CP}
   $$
   Substituting the selling price:
   $$
   1470 - \text{CP} = \frac{1}{6} \times \text{CP}
   $$

4. **Combining Terms**:
   To eliminate the fraction, we can multiply the entire equation by 6:
   $$
   6 \times 1470 - 6 \times \text{CP} = \text{CP}
   $$
   This simplifies to:
   $$
   8820 - 6 \times \text{CP} = \text{CP}
   $$

5. **Rearranging the Equation**:
   Now, we can combine like terms:
   $$
   8820 = 7 \times \text{CP}
   $$

6. **Solving for CP**:
   Dividing both sides by 7 gives us the cost price:
   $$
   \text{CP} = \frac{8820}{7} = 1260
   $$

### Conclusion:
The cost price of the exhaust fan is Rs 1,260.

### Meaning of $$ 75\% $$ Loss:
A $$ 75\% $$ loss means that the selling price is $$ 25\% $$ of the cost price. If the cost price is Rs 1,260, then a $$ 75\% $$ loss would imply:
$$
\text{Selling Price} = 0.25 \times \text{CP} = 0.25 \times 1260 = 315
$$
Thus, selling at a $$ 75\% $$ loss would mean selling the exhaust fan for Rs 315.
The cost price of the exhaust fan is Rs 1,260. A $$ 75\% $$ loss means selling the fan for Rs 315.

(d) What is the meaning of \( 75 \% \) loss? By selling an exhaust fan for Rs 1,470 , Mr. Ekaraj gains \( \frac{1}{6} \) of its cost price.

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