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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. $14$
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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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