physics about moment and force

Question

The two arms of a beam balance are of slightly different lengths. An unknown mass is weighed first on the left pan and then on the right pan. The two measurements are X and Y respectively. What is the actual mass in terms of X and Y?

Answer 1

Let the length of left arm be l1 and length of right arm be l2 and the unknown mass has mass M.
An unknown mass is weighed first on the left pan. It gives reading X.
Taking moment => Ml1=Xl2 --- (1)
and then on the right pan. It gives reading Y.
Taking moment => Yl1=Ml2 --- (2)
(1) / (2) gives
M/Y = X / M
M2 = XY
M = square root of (XY)