(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.

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.