Ravi made an error of 5% in excess while measuring the length of rectangle and an error of 8% deficit wad made while measuring the breadth . What is the percentage error in the area ?

Options

A. `-3%`
B. `-40%`
C. `-3.4%`
D. can't be determined

Answer

To find the percentage error in the area of the rectangle when there are errors in measuring the length and breadth, we can follow these steps:

### Step 1: Understand the Errors
- The length of the rectangle is measured with a 5% excess error.
- The breadth of the rectangle is measured with an 8% deficit error.

### Step 2: Define the Original Measurements
Let:
- The original length of the rectangle be \( L \).
- The original breadth of the rectangle be \( B \).

### Step 3: Calculate the Measured Length and Breadth
- The measured length (with a 5% excess) is:
\[ L' = L + 0.05L = 1.05L \]
- The measured breadth (with an 8% deficit) is:
\[ B' = B - 0.08B = 0.92B \]

### Step 4: Calculate the Original Area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 5: Calculate the Measured Area
The measured area \( A' \) using the incorrect measurements is:
\[ A' = L' \times B' = (1.05L) \times (0.92B) \]
Calculating this gives:
\[ A' = 1.05 \times 0.92 \times L \times B = 0.966 \times A \]

### Step 6: Calculate the Percentage Error in Area
The percentage error in the area can be calculated as:
\[ \text{Percentage Error} = \left( \frac{A' - A}{A} \right) \times 100\% \]
Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{0.966A - A}{A} \right) \times 100\% \]
\[ = \left( \frac{-0.034A}{A} \right) \times 100\% \]
\[ = -3.4\% \]

### Conclusion
Thus, the percentage error in the area of the rectangle is a decrease of **3.4%**.

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