Question

The distance between two places was 250 km. It was measured as 260 km, find the percentage error?

Answer 1

Hint: Find the difference in the original value and the calculated value. The difference between the original value and the measured value is known as the error. Use the formula of percentage error, $\dfrac{{{\text{Error}}}}{{{\text{Original value}}}} \times 100$ to calculate the required percentage error.

Complete step-by-step answer:
First of all calculate the difference in the correct distance and the wrong distance.
The correct distance is 250 km and the wrong distance is 260 km.
Hence, there is a difference of $260 - 250 = 10$km.
Therefore, 10 km is measured extra.
We will now find the percentage error.
Percentage error can be calculated as, $\dfrac{{{\text{Error}}}}{{{\text{Original value}}}} \times 100$
We have error as 10km, original value as 250 km.
On substituting the required value in the formula of percentage error, we get,
$\dfrac{{10}}{{250}} \times 100$
Solve the above expression to calculate the percentage error.
$\dfrac{1}{{25}} \times 100 = 4$
Therefore, there is an error of 4% when the distance is measured as 260 km and not 250 km.

Note: Percentage error can be calculated as, $\dfrac{{{\text{Error}}}}{{{\text{Original value}}}} \times 100$. Many students make mistakes by taking the final value in the formula of percentage error, that is taking 260 instead of 250 in this question. We can also say that the distance was measured 4% more than the actual distance.