If 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 10

C 40

D 70

Correct Answer: Option C

Let the numbers are \(x_{1,}x_{2,}.......x_{75}\)

By Hypothesis \(\frac{x_1+x_2+....x_{75}}{75}=35\) ....(i)

Mean of new numbers

= \(\frac{\left(x_1+5\right)+\left(x_2+5\right)+.......\left(x_{75}+5\right)}{75}\)

= \(\frac{x_1+x_2+......x_{75}+5\ast75}{75}\)

=\(\frac{x_1+x_2+......x_{75}}{75}+\frac{375}{75}=35+5=40\) By (i)