Question

The number of shot in a triangular pile is greater by $150$ than half the number of shot in a square pile, the number of layers in each being the same; find the number of shot in the lowest layer of the triangular pile.

Answer 1

Let 'n' be the no. of layers, then

No. of shots in triangular pile- $\frac{1}{2}\times$No. of shots in square pile$=150$

$\frac{n(n+1)(n+2)}{6}-\frac{1}{2}\times \frac{n(n+1)(2n+1)}{6}=150$

The no. of shots in the lowest layer is

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

$\frac{n(n+1)}{2}\{\frac{n+2}{3}-\frac{2n+1}{6}\}=150$

$\frac{n(n+1)}{2}\times \frac{1}{2}=150$

$\frac{n(n+1)}{2}=300$