In measuring the sides of a rectangle errors of $5$ % and $3$ % in excess are made. The error per cent in the calculated area is

8.35

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7.15

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8.15

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6.25

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Solution

The correct option is C $8.15$ %
$\Rightarrow$ Let actual sides of the rectangle be $x$ and $y$ respectively.
$\Rightarrow$ Measured sides are $x + 0.05 x = 1.05 x$ and $y + 0.03 y = 1.03 y$
$\Rightarrow$ Actual area = $x y$ .
$\Rightarrow$ Measured area = $(1.05) (1.03) x y = 1.0815 x y$

$\Rightarrow$ Error in area = $1.0815 x y - x y = 0.0815 x y$

$\Rightarrow$ Error percentage = $\frac{E r r o r i n a r e a}{A c t u a l a r e a} \times 100$ = $\frac{0.0815 x y}{x y} \times 100 = 8.15 %$

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