Question

The value of a triangular pile of $16lb$. shot is $51$; if the value of iron be $10s.6d$. per cwt, find the number of shot in the lowest layer.

Answer 1

The no. of shots in the pile $=\frac{51\times 20}{10\times \frac{1}{2}}\times \frac{112}{16}$

$=680$

So, no. of shots in triangular pile is:-

$\frac{n(n+1)(n+2)}{6}$

$\therefore \frac{n(n+1)(n+2)}{6}=680$

$n(n+1)(n+2)=6\times 17\times 40=15\times 16\times 17$

$\therefore n=15$

No. of shots in the lowest layer

$=\frac{15\times 16}{2}=120$