If the length of a rectangular plot of land is increased by $5 %$ and the breadth is decreased by $10 %$ , how much will its area increase or decrease?

6.5 %

increase

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5.5 %

decrease

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5.5 %

increase

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6.5 %

decrease

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Solution

The correct option is B $5.5 %$ decrease
Let length of plot $= l$
Breadth of plot $= b$
Area of plot $= l \times b$
Increased length $= l + \frac{5 l}{100} = \frac{105 l}{100} = 1.05 ℓ$
Decreased breadth $= b - \frac{10 b}{100} = 0.9 b$
New area $= (1.05 \times 0.9) l b = 0.945 l b$
Decrease in area $= \frac{l b - 0.945 l b}{l b} \times 100$
$= 0.055 \times 100 = 5.5 %$

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