Question

the mean of 10 numbers is 20 if 5 is subtracted from every number what will be the mean

Answer 1

15 is the new average.
solution......(20×10)-(5×10)/10
=200-50/10
=150/10
=15

Answer 2

Answer:

Let $\sf{x}_{1}$, $\sf{x}_{2}$, ... , $\sf{x}_{10}$ be the 10 numbers with their mean equal to 20. Then,

$\tt \bar x = \frac{1}{n} \\ \\ \implies \tt 20 = \frac{x_1 + x_2 + ... + x_10}{10} \\ \\ \tt \implies \: x_1 + x_2 + ... + x_10 = 200$

_______________________

New numbers are $\tt{x_1\:-\:5,\:x_2\:-\:5,\:...,\:x_10-5.}$ Let $\bar{X'}$ be the mean numbers. Then,

$\tt \bar x' = \frac{(x_1 - 5) + (x_2 - 5) + ... + (x_10 - 5)}{100} \\ \\ = \tt\frac{(x_1 + x_2 + ... + x_10) - 5 \times 10}{10} \\ \\ \tt \frac{200 - 50}{10} \\ \\ = 15$