A businessman uses a faulty balance of unequal arms of lengths x and y respectively. He sells W kg of tea to each customer. While selling to the 1 st and the 2 nd customers he keeps the counterpoising weight on the left pan and on the right pan respectively. Does he gain or lose?

A businessman uses a faulty balance of unequal arms of lengths x and y

1.	A businessman uses a faulty balance of unequal arms of lengths x and y respectively. He sells W kg of tea to each customer. While selling to the 1 st and the 2 nd customers he keeps the counterpoising weight on the left pan and on the right pan respectively. Does he gain or lose?
Answer» Solution :Suppose the lengths of the LEFT and the right arms of the balance are x and y respectively. For the first customer he places the counterpoising weight in the left pan. In this case the tea is placed in the other pan. Suppose `W_(1)` kg of tea BALANCES W kgweight. HENCE `Wxxx = W_(1)XXY` or, `W_(1)= (Wx)/(y)` For the SECOND customer he places the W kg counterpoising weight in the right pan. Suppose, in this case `W_(2)` kg tea is placed in the other pan. `:. W_(2)xxx= Wxxy` or, `W_(2)= (Wy)/(x)` The customers pay for 2 W kg but get `(W_(1)+W_(2))` kg of tea. `W_(1)+W_(2)-2W = (Wx)/(y)+(Wy)/(x)-2W` `=W((x)/(y)+(y)/(x)-2)=(W)/(xy)(x-y)^(2)` which is positive quantity. `:. (W_(1)+W_(2)) gt 2W`. Hence there is a loss for the business man.