The cost of 5 kgs of apples is ₹ 450. The cost of 12 dozen mangoes is ₹ 4,320 and the cost of 4 kgs of oranges is ₹ 240. What is the total cost of 8 kg of apples, 8 dozens of mangoes and 8 kg of oranges? [MAT—2012]

### Concept & Unitary Method Calculate the unit price for each commodity individually, then multiply by the requested quantity (8 units for each) to find the final aggregated cost. $$ \text{Cost} = (\text{Unit Price}) \times (\text{Quantity}) $$ ### Step-by-Step Solution * **Apples:** * Cost of 5 kg = ₹ 450 * Cost of 1 kg = $\frac{450}{5} = ₹ 90$ * Cost of 8 kg = $8 \times 90 = ₹ 720$ * **Mangoes:** * Cost of 12 dozen = ₹ 4320 * Cost of 1 dozen = $\frac{4320}{12} = ₹ 360$ * Cost of 8 dozen = $8 \times 360 = ₹ 2880$ * **Oranges:** * Cost of 4 kg = ₹ 240 * Cost of 1 kg = $\frac{240}{4} = ₹ 60$ * Cost of 8 kg = $8 \times 60 = ₹ 480$ * **Total Cost:** * Total = $720 + 2880 + 480$ * Total = $3600 + 480 = 4080$. ### Exam Strategy & Shortcut Instead of finding the unit price, use fractions to directly find the cost for 8 units: Apples: $\frac{8}{5} \times 450 = 8 \times 90 = 720$. Mangoes: $\frac{8}{12} \times 4320 = \frac{2}{3} \times 4320 = 2 \times 1440 = 2880$. Oranges: $\frac{8}{4} \times 240 = 2 \times 240 = 480$. Sum = $720 + 2880 + 480 = 4080$. ### Common Pitfall Be careful not to convert "dozens of mangoes" into individual mangoes. The initial price and the final requested price are both in "dozens", so treat a "dozen" as the base unit. ### Final Answer Therefore, the correct answer is **₹ 4,080**.