Answer
The mass of the sand should be 20 kg.
Work Step by Step
The center of gravity of the plank is 50.0 cm from the right end. This is a distance of 50.0 cm from the pivot.
The center of gravity of the sand is 37.5 cm from the left end. This is a distance of 62.5 cm from the pivot. Let $M$ be the mass of the sand.
$\sum \tau = 0$
$Mg~(0.625~m) - (25.0~kg)(g)(0.50~m) = 0$
$Mg~(0.625~m) = (25.0~kg)(g)(0.50~m)$
$M = \frac{(25.0~kg)(0.50~m)}{0.625~m}$
$M = 20~kg$
The mass of the sand should be 20 kg.
