A man sells two articles at ₹ 99 each. He gains $10\%$ on one and loses $10\%$ on the other. Then on overall basis he (P.C.S., 2006)

### Concept & Absolute Net Loss Calculation Similar to the previous problem, determine the overall percentage loss first, and then translate that percentage into the actual cash amount lost based on the Total Selling Price. $$ \text{Net Loss \%} = \frac{x^2}{100} $$ ### Step-by-Step Solution * Total Selling Price ($SP$) = ₹ 99 + ₹ 99 = ₹ 198. * Since SPs are identical and percentage gain ($10\%$) equals percentage loss ($10\%$), we find the overall loss percentage. * Net Loss \% = $\frac{10^2}{100} = \frac{100}{100} = 1\%$ loss. * This means the Total Selling Price represents $99\%$ ($100\% - 1\%$) of the Total Cost Price. * Let Total $CP$ be $x$. Then $99\%$ of $x = 198$. * $0.99x = 198 \implies x = \frac{198}{0.99} = 200$. * The Total Cost Price is ₹ 200, and the Total Selling Price is ₹ 198. * Absolute Loss = Total CP - Total SP = $200 - 198 = 2$. * The transaction results in a loss of ₹ 2. ### Exam Strategy & Shortcut Use the ratio method. The net loss is $1\%$, which is $\frac{1}{100}$. This means if CP is 100 units, Loss is 1 unit, and SP is 99 units. We know Total SP = 198. If 99 units = ₹ 198, then 1 unit = ₹ 2. The loss is exactly 1 unit, which equals ₹ 2. ### Common Pitfall Calculating the $1\%$ loss on the Total Selling Price (taking $1\%$ of 198 = 1.98) instead of recognizing that 198 represents $99\%$ of the original base (Cost Price). ### Final Answer Therefore, the correct answer is **loses ₹ 2**.