Approximation using unit rates: If three dozens mangoes cost ₹ 245, estimate the cost of 363 mangoes.

Difficulty: Medium

Correct Answer: ₹ 2400

Explanation:


Introduction / Context:
Estimation with proportional scaling is a key aptitude skill. We scale the known price for a fixed count to find an approximate price for a much larger count.



Given Data / Assumptions:

  • Cost for 3 dozens = 36 mangoes is ₹ 245.
  • Find approximate cost for 363 mangoes.
  • Assume constant unit price and allow rounding to the nearest reasonable option.


Concept / Approach:
Compute the unit price per mango as total cost divided by 36. Multiply by 363. Round to the closest offered option since the prompt requests an approximate cost.



Step-by-Step Solution:

Unit price ≈ 245 / 36 ≈ 6.8056Total cost ≈ 6.8056 * 363Breakdown: 6.8056 * 300 ≈ 2041.68; * 60 ≈ 408.336; * 3 ≈ 20.4168Sum ≈ 2041.68 + 408.336 + 20.4168 ≈ 2470.43Closest option to ₹ 2470 is ₹ 2400


Verification / Alternative check:
Use proportionality: 363/36 ≈ 10.0833. Then 10.0833 * 245 ≈ 2470.41, confirming the estimate above.



Why Other Options Are Wrong:
₹ 2000 and ₹ 2200 are too low relative to the computed estimate. ₹ 2600 overshoots more than ₹ 2400 does. ₹ 2400 is the nearest provided figure.



Common Pitfalls:
Forgetting that three dozens equals 36, rounding unit price too early, or multiplying by 12 by mistake.



Final Answer:
₹ 2400

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