Question

lf the arithmetic mean of seventy-five numbers is calculated, it is 35. If each number is increased by 5, then mean of new numbers is :

• A. 30
• B. 40
• C. 70
• D. 90

Answer 1

The correct option is B 40

Let the numbers be: $x_1,x_2,x_3,...\dots .x_{75}$

Then, $\frac{\sum _{i=1}^{75}{x}_i}{75}=35$

$\sum _{i=1}^{75}{x}_i=2625$ …………$\left(1\right)$

Now, numbers: $x_1+5,x_2+5,x_3+\mathrm{5...}\dots ..x_{75}+5$

$\frac{\sum _{i=1}^{75}(x_i+5)}{75}=?$

$\Rightarrow \frac{\sum _{i=1}^{75}{x}_i+5\times 75}{75}$

$=\frac{\sum _{i=1}^{75}{x}_i}{75}+\frac{5\times 75}{75}$

$=35+5$

$\therefore$New mean$=40$.