A dealer buys dry fruit at the rate of ₹ 100, ₹ 80 and ₹ 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity? (M.A.T., 2007)

### Concept & Profit Balancing in Mixtures When the overall transaction results in no gain no loss, the total profit earned on some parts must exactly equal the total loss incurred on the remaining parts to balance the books to zero. ### Step-by-Step Solution * Let the weights of the three types of dry fruit be 12 kg, 15 kg, and 20 kg. * Cost price (CP) of the three quantities: * 1st quantity: $12 \times 100 = 1200$ * 2nd quantity: $15 \times 80 = 1200$ * 3rd quantity: $20 \times 60 = 1200$ * Total CP of all dry fruits = $1200 + 1200 + 1200 = 3600$. * Total profit on the first two quantities is 20%. * Total CP of first two = $1200 + 1200 = 2400$. * Profit earned = $20\%$ of $2400 = 480$. * Since there is no overall gain or loss, the loss on the third quantity must exactly offset this profit. * Loss on the third quantity = 480. * Percentage loss on the third quantity = $\left(\frac{480}{1200}\right) \times 100 = 40\%$. ### Exam Strategy & Shortcut Notice that the total cost of each part is identical ($12 \times 100 = 1200$, $15 \times 80 = 1200$, $20 \times 60 = 1200$). Since the first two parts (which make up $\frac{2}{3}$ of the total cost) generated a 20% profit, the combined profit is $2 \times 20\% = 40\%$ relative to one part's base cost. To balance this to 0%, the third part (1 base cost) must absorb exactly a 40% loss. ### Common Pitfall A common mistake is trying to calculate the specific selling price per kg of each item individually, which introduces unnecessary complex variables and wastes significant time. ### Final Answer Therefore, the correct answer is **40%**.