360 bricks are stated in the …

Number of bricks in the bottom row=30. in the next row=29, and so on.

therefore, Number of bricks stacked in each row form a sequence 30, 29, 28, 27,... , which is an AP with first term , $a$=30  and common difference, $d$= 29 - 30 = -1.

Suppose number of rows is $n$, then sum of number of bricks in n rows should be 360

i.e. $S_n=360$ 

$\Rightarrow \frac{n}{2}[2 \times 30 + (n - 1)( - 1)] = 360$        {$S_n=\frac{n}{2}(2a+(n-1)d)$}

$\Rightarrow 720 = n(60 - n + 1)$

$\Rightarrow {\text{720 = 60n - }}{{\text{n}}^2} + n$

$\Rightarrow n^2 - 61n+720=0$

$\Rightarrow n^2 - 16n-45n+720=0$ [by factorisation]

$\Rightarrow n(n-16)-45(n-16)=0$

$\Rightarrow (n-16)(n-45)=0$

$\Rightarrow (n-16)=0$ or $(n-45)=0$

$\Rightarrow n=16$ or $n=45$

Hence, number of rows is either 45 or 16.

When, $n=16$,

$a_{16}=30+(16-1)(-1)$     {$a_n=a+(n-1)d$}

$=30-15=15$

When, $n=45$

$a_{45}=30+(45-1)(-1)$        {$a_n=a+(n-1)d$}

$=30-44=-14$ [$\because$ The number of logs cannot be neagtive]

Hence, the number of rows is 16 and number of logs in the top row is 15.