Percentage change in area – Length halved and breadth tripled: A rectangle has its length reduced to half and its breadth increased threefold. Find the overall percentage change in the area.
Aptitude
Area
Difficulty: Easy
Choose an option
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A20%
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B30%
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C40%
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D50%
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ENone of these
Answer
Correct Answer: 50%
Explanation
Introduction / Context:Percentage change in area due to independent percentage changes in dimensions can be calculated by multiplying scale factors.
Given Data / Assumptions:
- Original area A = L * B.
- New length = L/2; new breadth = 3B.
Concept / Approach:New area A' = (L/2) * (3B) = (3/2) * (L * B) = 1.5A ⇒ 50% increase.
Step-by-Step Solution:
Scale factor = (1/2) * 3 = 3/2 = 1.5.Percentage change = (1.5 − 1) * 100% = 50% increase.Verification / Alternative check:Take L = 10, B = 10 ⇒ A = 100. New L = 5, B = 30 ⇒ A' = 150 ⇒ 50% rise.
Why Other Options Are Wrong:20%, 30%, 40% do not match the multiplicative effect of the two independent changes.
Common Pitfalls:Adding percentage changes instead of multiplying factors; i.e., (−50%) + (+200%) ≠ +150% area; use factors.
Final Answer:50%