The average of $x$ numbers is $3 x$ . If $(x - 1)$ is subtracted from each given number, what will be the new average?

3 (x - 1)

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2 x + 1

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2 x - 1

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Data inadequate

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Solution

The correct option is B $2 x + 1$
Solution:-
Given:- Average of x numbers $=$ $3 x$
$\Rightarrow \frac{Sum of numers}{x} = 3 x$
$\Rightarrow Sum of numbers = 3 x^{2}$
If each no. is subtracted from $(x - 1)$ we get
sum of numbers after subtracting $(x - 1)$ = Sum of numbers $- x - (x - 1)$
$=$ $3 x^{2} - x (x - 1)$
$=$ $3 x^{2} - x^{2} + x = 2 x^{2} + x$
New average = $\frac{Sum of numbers after subtracting (x - 1) from each}{x}$
$=$ $\frac{2 x^{2} + x}{x} = 2 x + 1$
B) $2 x + 1$

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