If $r$ is a real number that $|r| < 1$ and if $a = 5 (1 - r)$ , then

$0 < a < 5$

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$- 5 < a < 5$

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$0 < a < 10$

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$- 10 < a < 10$

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Solution

The correct option is C
$0 < a < 10$

Explanation for the correct option:
Given $|r| < 1$ which implies $- 1 < r < 1$
From the given relation, we have
$a = 5 (1 - r) \dots (1)$
Multiply the above inequality by $- 1$ , we get
$1 > - r > - 1$
This can be rewritten as $- 1 < - r < 1$
Then add $1$ in the LHS, RHS, and the variable $r$ , then we have
$0 < 1 - r < 2$
Finally, multiply the inequality by $5$ ,
$0 < 5 (1 - r) < 10$
From equation $(1)$ ,
$0 < a < 10$
Hence, the correct option is (C).

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