A house and a shop were sold for ₹ 1 lakh each. In this transaction, the house sale resulted into $20\%$ loss whereas the shop sale resulted into $20\%$ profit. The entire transaction resulted in

### Concept & Absolute Net Loss Calculation When asked for the *absolute cash amount* of the loss (rather than just the percentage) in a "same SP, same percentage gain/loss" scenario, you must calculate the exact aggregate Cost Price and subtract the aggregate Selling Price. $$ \text{CP} = \frac{\text{SP}}{1 \pm \frac{\text{Profit/Loss \%}}{100}} $$ ### Step-by-Step Solution * Total Selling Price ($SP$) = ₹ 1 lakh + ₹ 1 lakh = ₹ 2 lakhs. * Calculate Cost Price of the house ($CP_h$): Loss = $20\%$, so $SP_h = 0.8 \times CP_h$ $1 = \frac{4}{5} \times CP_h \implies CP_h = \frac{5}{4}$ lakhs (or $1.25$ lakhs) * Calculate Cost Price of the shop ($CP_s$): Profit = $20\%$, so $SP_s = 1.2 \times CP_s$ $1 = \frac{6}{5} \times CP_s \implies CP_s = \frac{5}{6}$ lakhs * Total Cost Price ($CP$) = $CP_h + CP_s$ Total $CP = \frac{5}{4} + \frac{5}{6} = \frac{15}{12} + \frac{10}{12} = \frac{25}{12}$ lakhs. * Since Total CP ($\frac{25}{12} \approx 2.083$) is greater than Total SP (2), there is a loss. * Net Loss = Total CP - Total SP Net Loss = $\frac{25}{12} - 2 = \frac{25}{12} - \frac{24}{12} = \frac{1}{12}$ lakh. ### Exam Strategy & Shortcut First, determine the net loss percentage using the theorem: $\frac{20^2}{100} = 4\%$ loss. This means Total SP is $96\%$ of Total CP. Total SP = 2 lakhs. $96\%$ of Total CP = 2 lakhs. We want to find the absolute loss, which is the remaining $4\%$ of Total CP. If $96\% = 2$, then $4\% = \frac{2}{96} \times 4 = \frac{2}{24} = \frac{1}{12}$ lakh. This skips finding individual CPs! ### Common Pitfall Automatically selecting "no loss, no gain" due to the identical percentages, or calculating the $4\%$ net loss but failing to convert that percentage back into the absolute monetary value requested by the options. ### Final Answer Therefore, the correct answer is **loss of ₹ $\frac{1}{12}$ lakh**.