Unitary method: If 24 oranges cost ₹ 72, find the cost of 120 oranges (assume a constant rate).
Correct Answer: ₹ 360
Introduction / Context:This is a direct proportion cost question. When unit price is constant, total cost scales linearly with quantity. We apply the unitary method to find the cost of a larger batch.Given Data / Assumptions:
- 24 oranges cost ₹ 72.
- Find cost for 120 oranges.
- Assume uniform price per orange.
Concept / Approach:First compute the price per orange, then multiply by 120 to obtain the total cost for that quantity.Step-by-Step Solution:
Price per orange = 72 / 24 = ₹ 3.Cost of 120 = 120 × 3 = ₹ 360.Verification / Alternative check:Proportion scaling: 120 is 5 times 24, so the cost is also 5 times ₹ 72, i.e., ₹ 360. This matches the unit rate calculation.Why Other Options Are Wrong:
- ₹ 180: Equals half of ₹ 360; would correspond to 60 oranges, not 120.
- ₹ 172 and ₹ 500: Do not align with the linear scaling from the given unit cost.
Common Pitfalls:Forgetting to scale the cost by the same factor as the quantity (here, 5×). Always confirm by comparing ratios to ensure consistency.Final Answer:
₹ 360