1. The robbers filled a chest to the brim with gold and silver sand, with twice as much gold sand by volume as silver sand. Ali-Baba calculated that if half of the silver sand were removed and the chest topped up with gold sand, the value of the chest would increase by 20 percent. By what percentage and how would the value of the chest change if half of the gold sand were removed and the chest topped up with silver sand?
Answer. It will decrease by $40 \%$. Solution. Let the initial volume of silver sand in the chest be $A$, the cost of a unit volume of gold sand be $x$, and the cost of a unit volume of silver sand be $y$. Then the initial cost of the chest is $2 A x+A y$. The cost of the chest according to Ali-Baba's calculations is $2.5 A x+0.5 A y$, which leads to the equation $1.2(2 A x+A y)=2.5 A x+0.5 A y$ and the ratio $x=7 y$. Then in the second case, the cost of the chest will be $A x+2 A y=9 A y$, which, relative to the initial cost, equal to $2 A x+A y=15 A y$, constitutes $60 \%$.