Percentage change in area – Length halved and breadth tripled:\nA rectangle has its length reduced to half and its breadth increased threefold. Find the overall percentage change in the area.

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:

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%