David gets on the elevator at the $11$ th floor of a building and rides up at the rate of $57$ floors per minute. At the same time, Albert gets on an elevator at the $51$ st floor of the same building and rides down at the rate of $63$ floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

19

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30

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Solution

The correct option is B $30$
Suppose their paths cross after $x$ minutes.
Then, $11 + 57 x = 51 - 63 x \Leftrightarrow 120 x = 40 \Leftrightarrow x = \frac{1}{3}$ .
Number of floors covered by David in $\frac{1}{3}$ min. $= (\frac{1}{3} \times 57) = 19$ .
So, their paths cross at $(11 + 19)$ th i.e. $30$ th floor.

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The correct option is B 30Suppose their paths cross after x minutes.Then, 11+57x=51−63x⇔120x=40⇔x=13.Number of floors covered by David in 13 min. =(13×57)=19.So, their paths cross at (11+19)th i.e. 30th floor.