A 4 m long plank AB with a mass of 50 kg is placed on two props. One of the props is at A and the other is at a distance of 0.5m from B. A person with a mass of 45 kg is standing on the plank 0.8 m from A. What are the forces on the two props?

Let the midpoint of the plank be O. The plank is at rest and hence is at equilibrium. Taking moments about O.

$-P\times2+45\times1.2+50\times0+Q\times1.5=0$

$\Rightarrow2P-1.5Q=54\ldots\ldots\ldots(i)$

Resolving vertically,

$P+Q-45-50=0\Rightarrow P+Q=95\ldots\ldots\ldots(ii)$

Solving (i) and (ii), we have $P=\ \frac{393}{7}kg-wt,\ Q=\frac{272}{7} kg-wt$