Xavier Aptitude Test 2020 Paper

Question : 51 of 100

Marks: +1, -0

Two lighthouses, located at points $\A$ and $\B$ on the earth, are $60 \feet$ and $40 \feet$ tall respectively. Each lighthouse is perfectly vertical and the land connecting $\A$ and $\B$ is perfectly flat. The top most point of the lighthouse at $\A$ is $\A’$ and of the lighthouse at $\B$ is $\B’$ . Draw line segments $\A’\B$ and $\B’\A$ , and let them intersect at point $\C’$ . Drop a perpendicular from $\C’$ to touch the earth atpoint $\C$ . What is the length of $\CC’$ in feet?

$20$
$25$
$30$
$24$
The distance between $\A$ and $\B$ is also needed to solve this

Validate

Solution:

Triangle

\ACC'

is similar to triangle

\ABB'

Considering

\AC = a

\BC = b

\CC' = h

\AA'

is given as

60

\BB'

is given to be

40

{\AC}/{\AB} = {\CC'}/{\BB'} = h/40.

a/{a+b}= h/40

...(i)

Similarly triangle

\BCC'

is similar to

\BAA'

{\BC}/{\AB} = {\CC'}/{\AA'} = h/60

b/{a+b}= h/60

...(ii)

Adding equition (1) and (2)

h/40 + h/60=1

1/h=(1/40+1/60)

h=24

Using crossed ladder theorem

1/\CC'= 1/\AA' + 1/{BB'} =1/60 + 1/40 = 5 /120 =24.

Go to Question:

Prev Question

Next Question