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Q.

A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank.


                                                                                                              tree                      8m

                                  21m

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a

24.9375

m

b

24.575

m

c

2.49375

m

d

249.375

m

answer is A.

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Detailed Solution

Given a water tank that casts a shadow 21 m long and a tree of height 9.5 m that casts a shadow 8 m long at the same time.
We know that the lengths of the shadows are directly proportional to their heights.
We need to find the height of the tank.
Assume that height of tank is

h

m.
Using the given information that lengths of the shadows are directly proportional to their heights hence ratio of lengths of the shadows and height would be constant.

\frac{length of shadow}{height} = constant

Equate ratio of 8 m long shadow and 9.5 height with the ratio of 21 m long shadow and

h

m height of tank to solve for

h

.

\frac{8}{9.5} = \frac{21}{h}

\Rightarrow h = \frac{21 \times 9.5}{8}

\Rightarrow h = 24.9375

Height of tank is 24.9375 m.
Hence, the correct option is 1.

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