A TV manufacturer sells an item to a wholesaler at a profit of $8\%$. The wholesaler sells it to a retailer at a profit of $10\%$. The retailer in turn sells it to the customer for ₹$11,050$ making a profit of $15\%$. What is the manufacturer's purchasing price? (Assume only whole numbers)

Let the purchasing price (cost price) for the manufacturer be $P$.Manufacturer sells to wholesaler at $8\%$ profit $⟹\text{Price}=P\times 1.08$ Wholesaler sells to retailer at $10\%$ profit $⟹\text{Price}=P\times 1.08\times 1.10$ Retailer sells to customer at $15\%$ profit $⟹\text{Price}=P\times 1.08\times 1.10\times 1.15$ We are given that the final selling price to the customer is ₹$11,050$:
$$P\times \frac{108}{100}\times \frac{110}{100}\times \frac{115}{100}=11050$$
$$P\times \frac{27}{25}\times \frac{11}{10}\times \frac{23}{20}=11050$$
$$P\times \frac{27\times 11\times 23}{5000}=11050$$
Notice that $11050÷23=480.43$, let's simplify carefully:
$$27\times 11\times 23=6831$$
$$P=\frac{11050\times 5000}{6831}$$
$$P=\frac{55250000}{6831}\approx 8088.13$$
Since we assume only whole numbers, the purchasing price is approximately ₹$8,088$.