Rakesh is the owner of a rectangular field. Because of the construction of an expressway near his field, the length and breadth of his field are reduced by 30% and 10%, respectively. What is the percentage decrease in the area of his field?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 37%.
Let's assume the original length and breadth of the field are L and B, respectively.
Original Area: Original Area = L × B
New Dimensions:
⇒ New Length = L - 30% of L = 0.7L
⇒ New Breadth = B - 10% of B = 0.9B
⇒ New Area: New Area = 0.7L × 0.9B = 0.63LB
⇒ Decrease in Area: Decrease = Original Area - New Area = LB - 0.63LB = 0.37LB
Percentage Decrease:
⇒ Percentage Decrease = (Decrease / Original Area) × 100 = (0.37LB / LB) × 100 = 37%
Therefore, the area of the field decreases by 37%.