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${If the arithmetic mean of the numbers x}_{1}, x_{2}, x_{3}, \dots, x_{k} i s \bar{x}, t h e n t h e a r i t h m e t i c m e a n o f t h e n u m b e r s$
$a x_{1} + b, a x_{2} + b, a x_{3} + b . . . . . . . . . . a x_{n} + b,$
$w h e r e a, b a r e t w o c o n s t a n t s, w o u l d b e$

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a

x

b

nax+nb

c

ax

d

ax+b

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detailed solution

Correct option is D

Required mean is ax1+b+ax2+b+⋯+axn+bn =ax1+x2+⋯+xnn+b=ax¯+b ∵x1+x2+⋯+xnn=x¯

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