Question

In measuring the side of a square, an error of 5% in excess is made. The error % in the calculated area is,

• A. \(10.75%\)
• B. \(10.25%\)
• C. \(10.50%\)
• D. \(10.00%\)
• E. \(11.25%\)

Answer 1

The Correct Option is B

Concept: If a quantity has an error of \(x%\), then for square (area): \[ \text{Error in area} = (1 + \frac{x}{100})^2 - 1 \]
Step 1: Given error in side.
\[ \text{Error} = +5% \]
Step 2: Apply formula.
\[ \text{Error in area} = (1.05)^2 - 1 \]
Step 3: Calculate.
\[ (1.05)^2 = 1.1025 \] \[ \text{Error} = 1.1025 - 1 = 0.1025 = 10.25% \]
Step 4: Option analysis.

• (A) 10.75%: Incorrect $\times$
• (B) 10.25%: Correct \checkmark
• (C) 10.50%: Incorrect $\times$
• (D) 10.00%: Ignoring square effect $\times$
• (E) 11.25%: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).