Question

In measuring the sides of a rectangular plot, one side is taken 5% in excess and the other 6% in deficit. The error percent in area calculated, of the plot, is ........

• A. 1.3%
• B. 1%
• C. 1.5%
• D. 3%

Hint:

In percentage error problems involving areas, the total error in area is the sum of the percentage errors in each dimension.

Answer 1

The Correct Option is A

Let the actual sides of the rectangular plot be $x$ and $y$. - The length is increased by 5%, so the measured length will be $1.05x$. - The width is decreased by 6%, so the measured width will be $0.94y$. The error in the area is given by the difference in the area calculated using the erroneous measurements and the actual area: $$\text{Error in area} = (1.05x \times 0.94y) - (x \times y)$$ Simplifying the expression: $$\text{Error in area} = 0.987xy - xy = (0.987 - 1)xy = -0.013xy$$ Thus, the error in area is $-1.3$. So, the error percent in the area is 1.3%.

Step 2: Final Answer The correct answer is (a) 1.3%. Final Answer: The correct answer is (a) 1.3%.