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An elevator has a weight limit of $630$ kg. It is carrying a group of people of whom the heaviest weighs $57$ kg and the lightest weighs $53$ kg. What is the maximum possible number of people in the group?

1. $12$
2. $13$
3. $11$
4. $14$

Given that, Weight limit of elevator $= 630\;\text{kg}$

• The lightest person's weight  $= 53 \;\text{kg}$
• The heaviest person's weight   $= 57 \;\text{kg}$

We can write, $53 + \underbrace{\ldots \ldots}_{\text{Weights of$n$people}} + 57 = 630$

In order to have maximum people in the lift, all the remaining people should be of the lightest weight possible, which is  $53 \;\text{kg}.$

Suppose there are $n$ people in the elevator.

Then, $53 + n(53) + 57 < 630$

$\Rightarrow 53n < 520$

$\Rightarrow n < \frac{520}{53}$

$\Rightarrow n < 9.811$

$\Rightarrow n_{\text{max}} = \left \lfloor 9.811 \right \rfloor$

$\Rightarrow n_{\text{max}} = 9$

$\therefore$ The maximum number of people in the group $= n_{\text{max}} + 2 = 9 + 2 = 11.$

Correct Answer $: \text{C}$

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