A person bought some articles at the rate of 5 per rupee and the same number at the rate of 4 per rupee. He mixed both the types and sold at the rate of 9 for 2 rupees. In this business he suffered a loss of ₹ 3. The total number of articles bought by him was

### Concept & Formula Use the LCM of item quantities to create a "standard batch" size. Calculate the loss on this standard batch, then scale it up to match the actual given loss to find the true total quantity. $$\text{Scaling Factor} = \frac{\text{Actual Total Loss}}{\text{Loss on LCM Batch}}$$ ### Step-by-Step Solution * **Given:** CP1 = 5 for ₹ 1. CP2 = 4 for ₹ 1. SP = 9 for ₹ 2. Equal quantities bought. Total Loss = ₹ 3. * **Calculation:** 1. Find the LCM of 5, 4, and 9, which is 180. 2. Assume he buys 180 articles of each type. Total batch size = 360 articles. 3. CP of first 180 articles = $\frac{1}{5} \times 180 = \text{₹ } 36$ 4. CP of second 180 articles = $\frac{1}{4} \times 180 = \text{₹ } 45$ 5. Total CP for 360 articles = $36 + 45 = \text{₹ } 81$ 6. SP of 360 articles = $\frac{2}{9} \times 360 = 2 \times 40 = \text{₹ } 80$ 7. Loss on this standard batch = $81 - 80 = \text{₹ } 1$. 8. If a loss of ₹ 1 corresponds to 360 articles, then a total loss of ₹ 3 corresponds to $360 \times 3 = 1080$ articles. ### Exam Strategy & Shortcut Using the LCM batch method is the fastest and most foolproof strategy. By finding the baseline loss for a convenient integer quantity, scaling to the target loss becomes a simple multiplication, avoiding any complex algebraic fractions. ### Common Pitfall A common mistake is forgetting to double the assumed quantity when calculating the total cost. If you assume 180 items of each type, the total inventory being sold is 360 items, not 180. ### Final Answer Therefore, the correct answer is **1080**.