Question

The weight of a sand bag is 40 kg. In a hurry, it was weighed as 40.8 kg. The error percentage is
a. 1%
b. 0.5%
c. 1.5%
d. 2%

Answer 1

Hint: In order to find the correct solution of this question, we should know about the concept of error percentage, which is the difference between the estimated number and the actual number when compared to the actual number expressed in the percent format. By using this concept we can find the solution of this question.

Complete step-by-step answer:
In this question, we have been asked to find the percentage error of a sand bag which originally weighs 40 kg, but in a hurry, it was weighed as 40.8 kg. To solve this question, we should know the concept of error percentage, that is, the difference between the estimated number and the actual number when compared to the actual number expressed in the percent format. Mathematically, we can express this concept as,
$\text{Percentage formula=}\left| \dfrac{\text{expected value - observed value}}{\text{expected value}} \right|\text{ }\!\!\times\!\!\text{ 100 }\!\!%\!\!\text{ }$
Now, according to the question, we can say that the expected value is 40 kg and the observed value is 40.8 kg. So, we can write the percentage error of the sandbag as follows.
Percentage error = $\left| \dfrac{40-40.8}{40} \right|\times 100%$
Now, we will simplify it to get the final answer. So, we get
Percentage error = $\left| \dfrac{-0.8}{40} \right|\times 100%=\left| -0.02 \right|\times 100%$
Now, we know that $\left| -a \right|=a$. So, we can write,
Percentage error = 0.02 $\times $ 100%
Percentage error = 2%
Hence, we get the percentage error of the sandbag as 2%. Therefore, option (d) is the correct answer.

Note: While solving this question, we need to remember that error percentage is calculated by using the formula, $\text{Percentage formula=}\left| \dfrac{\text{expected value - observed value}}{\text{expected value}} \right|\text{ }\!\!\times\!\!\text{ 100 }\!\!%\!\!\text{ }$. We need to remember that the modulus sign is important, otherwise it will give us the wrong answer. Also, sometimes we might get confused with the formula and end up writing the observed value as the expected value and vice-versa, which will give us the wrong answer.