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:

When the dimensions are altered by a certain percentage, calculate the area by multiplying the altered dimensions and then find the error by comparing the calculated area with the actual area.

Answer 1

The Correct Option is A

Let the actual dimensions of the rectangular plot be \( l \) (length) and \( b \) (breadth). The area is given by: \[ A = l \times b \] Now, the length is measured with a 5% excess, so the measured length is \( l \times (1 + 0.05) = 1.05l \), and the breadth is measured with a 6% deficit, so the measured breadth is \( b \times (1 - 0.06) = 0.94b \). The calculated area using the measured values is: \[ A_{\text{calculated}} = 1.05l \times 0.94b = 0.987l \times b = 0.987A \] So, the error in area is: \[ \text{Error percent} = \frac{A_{\text{calculated}} - A}{A} \times 100 = \frac{0.987A - A}{A} \times 100 = -1.3% \] Thus, the error percent in the area is 1.3%. The correct answer is (1) 1.3%.