The percentage change in the area of a rectangular field, if its lengt

1.	The percentage change in the area of a rectangular field, if its length is increased by 40% and breadth is decreased by 10%, is1. 26% increase2. 30% decrease3. 30% increase4. None of the above
Answer» Correct Answer - Option 1 : 26% increase Formula used Area of rectangle = length × breadth Calculation Let length of rectangle = L and Breadth of rectangle = B Initial area= L × B Final length =L + (40/100) L = 1.4 L Final breadth = B - (10/100) B = 0.9 B Final area = 1.4 L × 0.9 B ⇒ 1.26 L × B Change in area = 1.26 (L × B) - (L × B) ⇒ 0.26 L × B ∴ Percentage Change in area = [(0.26 L × B)/(L × B)] × 100 ⇒ 26% increase Alternate method- Length - increased 40% = +40% Breathe - decrease 10% = -10% % change in area = L + B + L × B/100 = +40 + (-10) + (+40) × (-10) / 100 = +30 - 4 = +26 = Increased by 26%

The percentage change in the area of a rectangular field, if its length is increased by 40% and breadth is decreased by 10%, is1. 26% increase2. 30% decrease3. 30% increase4. None of the above

Answer» Correct Answer - Option 1 : 26% increase

Formula used

Area of rectangle = length × breadth

Calculation

Let length of rectangle = L and Breadth of rectangle = B

Initial area= L × B

Final length =L + (40/100) L = 1.4 L

Final breadth = B - (10/100) B = 0.9 B

Final area = 1.4 L × 0.9 B

⇒ 1.26 L × B

Change in area = 1.26 (L × B) - (L × B)

⇒ 0.26 L × B

∴ Percentage Change in area = [(0.26 L × B)/(L × B)] × 100

⇒ 26% increase

Alternate method-

Length - increased 40% = +40%

Breathe - decrease 10% = -10%

% change in area = L + B + L × B/100

= +40 + (-10) + (+40) × (-10) / 100

= +30 - 4 = +26 = Increased by 26%