CAT 2017

Slot 1

QA

Question & Solution

1. Concept Used

• Topic: Arithmetic – Maximization under Constraints
• Formula: $$\text{Total Weight} = W_{\text{heaviest}} + W_{\text{lightest}} + (n \times W_{\text{lightest}}) \leq 630$$

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2. Calculation

We are given that the elevator's maximum weight limit is 630 kg, the heaviest person weighs 57 kg, and the lightest person weighs 53 kg.

To maximize the number of people, we must minimize the total weight carried. Since the heaviest (57 kg) and lightest (53 kg) persons are already fixed and must be included, all remaining people should weigh as little as possible — i.e., each should weigh the minimum possible, which is 53 kg.

Let the number of additional people (besides the heaviest and lightest) be (n). Then the total weight is:

$$57 + 53 + 53n \leq 630$$

$$110 + 53n \leq 630$$

$$53n \leq 520$$

$$n \leq \frac{520}{53} \approx 9.81$$

Since (n) must be a whole number, we take (n = 9).

Verification: $$57 + 53 + 53 \times 9 = 110 + 477 = 587 \leq 630 \checkmark$$

If (n = 10): $$57 + 53 + 530 = 640 > 630 \times$$

So the maximum total number of people $$= 1 (\text{heaviest}) + 1 (\text{lightest}) + 9 (\text{additional}) = 11$$

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3. Solution

Answer = 11 ✅

The maximum possible number of people in the elevator is 11.