Question

If the number of shot in a triangular pile is to the number of shot in a square pile of double the number of courses as $13$ to $175$; find the number of shot in each pile.

Answer 1

$\frac{n(n+1)(n+2)}{6}\times \frac{6}{2n(2n+1)(4n+1)}=\frac{13}{175}$

$\frac{(n+1)(n+2)}{2(2n+1)(4n+1)}=\frac{13}{175}$

$\Rightarrow 11n^2-123n-108=0$

$\Rightarrow (11n+9)(n-12)=0$

$\therefore n=12$

$\therefore$No. of shots in triangular pile is :-

$=\frac{12\times 13\times 14}{6}=364$

No. of shots in square pile$=\frac{24\times 25\times 49}{6}$

$=4900$