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In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years namely $2001, 2002$ and $2003.$ If floods are again expected in $2004,$ the number of huts expected to be destroyed is:

1. Less than the number of huts existing at the beginning of $2001.$
2. Less than the total number of huts destroyed by floods in $2001$ and $2003.$
3. Less than the total number of huts destroyed by floods in $2002$ and $2003.$
4. More than the total number of huts built in $2001$ and $2002.$

Let the number of huts at the beginning of 2001 be x.

year Inital Number of Huts  Number of Huts Destroyed Number of Huts Rebuilt Total number of huts After Rebuilt
2001 x $\frac{x}{2}$ x $\frac{3x}{2}$
2002 $\frac{3x}{2}$ $\frac{3x}{4}$ $\frac{3x}{2}$ $\frac{9x}{4}$
2003 $\frac{9x}{4}$ $\frac{9x}{8}$ $\frac{9x}{4}$ $\frac{27x}{8}$
2004 $\frac{27x}{8}$ $\frac{27x}{16}$ $\frac{27x}{8}$ $\frac{81x}{16}$

A.False  $\frac{27x}{16}$ > x

B.False  $\frac{27x}{16}$ > $\frac{x}{2}$ + $\frac{9x}{8}$  = $\frac{27x}{16}$ >$\frac{13x}{8}$

C.True    $\frac{27x}{16}$ < $\frac{3x}{4}$ + $\frac{9x}{8}$ = $\frac{27x}{16}$ < $\frac{15x}{8}$

D.False $\frac{27x}{16}$ < x+ $\frac{3x}{2}$ =$\frac{27x}{16}$ < $\frac{5x}{2}$

Hence,Option(C)Less than the total number of huts destroyed by floods in 2002 and 2003.

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C) and D) both could be the answer
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how?

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