Question

The weight of a sandbag is 40 kg. In a hurry, it weighed 40.8 kg. The error percentage is:
(a) 1 %
(b) 0.5 %
(c) 1.5 %
(d) 2 %

Answer 1

Hint: To solve the question given above, we have to find out what error and error percentage is. We will calculate the error and then we will divide this value of error by the true weight of the sand bag to get the error percentage.

Complete step by step solution:
Before solving the question, we must know what an error is. An error is a difference between the true value of data and the mistaken value of the data. In our case, the true value of the data is equal to the actual weight of the sandbag which is equal to 40 kg. The mistaken value in our case is equal to the weight which is measured in a hurry and it is equal to 40.8 kg. The formula of the error is given as follows:
Error = |Mistaken Value – True Value|
In our case, the error will be the following,
Error = |Weight measured in a hurry – Actual Weight|
Now, we know that,
Weight measured in a hurry = 40.8 kg
True Weight = 40 kg
Thus, we will get,
\[\Rightarrow \text{ Error }=\left| 40.8kg-40kg \right|\]
\[\Rightarrow \text{ Error }=\left| 0.8kg \right|\]
\[\Rightarrow \text{ Error }=0.8kg\]
Now, we have to find the error percentage. The error percentage is obtained by dividing the error by the true value of the data and multiplying it by 100. Thus, the formula of the error percentage is:
\[\text{Error Percentage}=\dfrac{\text{Error}}{\text{True Value}}\times 100\text{ Percentage}\]
\[\Rightarrow \text{Error Percentage}=\dfrac{\text{Error}}{\text{Actual Weight of Sandbag}}\times 100\text{ Percentage}\]
\[\Rightarrow \text{Error Percentage}=\dfrac{0.8kg}{40kg}\times 100\text{ Percentage}\]
\[\Rightarrow \text{Error Percentage}=\dfrac{0.8\times 100}{40}\text{ Percentage}\]
\[\Rightarrow \text{Error Percentage}=\dfrac{80}{40}\text{ Percentage}\]
Therefore, Error Percentage = 2 %.
Hence, option (d) is the right answer.

Note: It is important that to obtain the error percentage, we divide the error by the actual value of the data and not the mistaken value of the data because the error is always calculated with respect to the true value of the data and not the mistaken value of the data.