A video magazine distributor made 3500 copies of the March issue of the magazine at a cost of ₹ 350000. He gave 500 cassettes free to some key video libraries. He also allowed a 25% discount on the market price of the cassette and gave one extra cassette free with every 29 cassettes bought at a time. In this manner, he was able to sell all the 3500 cassettes that were produced. If the market price of a cassette was ₹ 150, then what is his gain or loss percent for the March issue of video magazine?

### Concept & Revenue Calculation To find the overall profit or loss percentage, we must compare the total initial cost to the total revenue generated from the paid cassettes after all discounts and free offers are accounted for. ### Step-by-Step Solution - Total Cost Price (CP) for 3500 cassettes = Rs. 350,000. - Cassettes given free initially = 500. - Remaining cassettes for sale = $3500 - 500 = 3000$. - The offer is "buy 29, get 1 free". This means for every batch of 30 cassettes, 29 are paid for. - Number of 30-cassette batches in the remaining 3000 = $\frac{3000}{30} = 100$ batches. - Number of cassettes actually paid for = $100 \text{ batches} \times 29 \text{ paid cassettes/batch} = 2900$ cassettes. - Market Price (MP) per cassette = Rs. 150. - Discount allowed = $25\%$. - Selling Price (SP) per cassette = $150 \times (1 - 0.25) = 150 \times 0.75 = \text{Rs. } 112.5$. - Total Revenue (Total SP) = $2900 \times 112.5 = \text{Rs. } 326,250$. - Since Total SP < Total CP, there is a loss. - Loss = $\text{Total CP} - \text{Total SP} = 350,000 - 326,250 = \text{Rs. } 23,750$. - Loss Percentage = $(\frac{\text{Loss}}{\text{Total CP}}) \times 100 = (\frac{23750}{350000}) \times 100$. - Loss Percentage = $\frac{237.5}{35} \approx 6.78\%$, which rounds to $6.8\%$. ### Exam Strategy & Shortcut Track only the paid units. Total units = 3500. Free = 500. Remaining = 3000. Under the $29+1$ scheme, the paid fraction is $\frac{29}{30}$. Paid units = $3000 \times \frac{29}{30} = 2900$. Price per unit after $25\%$ off on 150 = $112.5$. Total Revenue = $2900 \times 112.5 = 326,250$. Loss = $350k - 326.25k = 23.75k$. $\%$ Loss = $\frac{23.75}{350} \times 100 \approx 6.8\%$. ### Common Pitfall Forgetting to subtract the initial 500 free cassettes before applying the "buy 29 get 1 free" scheme, or calculating revenue on all 3000 remaining cassettes, ignoring the fact that 1 in every 30 is free. ### Final Answer Therefore, the correct answer is **6.8% loss**.