Question

The average weight of a sample of $10$ apples is $62g$. Later it was found that the weighing machine has shown the weight of each apple $10g$ more. The correct average weight of an apple is

• A. $54g$
• B. $52g$
• C. $62g$
• D. $56g$

Answer 1

The correct option is B $52g$

$\begin{array}{c}Averageweightof10applesis62g.\\ \Rightarrow \frac{A_1+A_2+A_3+.........+A_{10}}{10}=62g\\ \Rightarrow A_1+A_2+A_3+...........+A_{10}=62g\\ \Rightarrow newweightofapplesare\left(A_1-10\right),\left(A_2-10\right),.........\left(A_{10}-10\right)\\ \Rightarrow Averageofnewweightofapples=\frac{\left(A_1-10\right)+\left(A_2-10\right)+.....+\left(A_{10}-10\right)}{10}\\ =\frac{\left(A_1+A_2+A_3+..........+A_{10}\right)-100}{10}=\frac{\left(620-100\right)}{10}\\ \begin{array}{c}Averageofnew\\ weightofapples\end{array})=\frac{520}{10}=52g.\end{array}$